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Comments: 99 Pages. Expanded and Presented Article's Version at "The 2016 GRavitational-Wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), Sorbonne University, 'Paris VI - UPMC, CNRS, LERU, EUA', Paris, France (2016). 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) ; International audience ; In Part I (pp. 1-10) of this article, I provide a general analysis of a number of current discontinuous approaches to fundamental physics. In Part II (the main part, pp. 11-99, Ref. [37]), as a new mathematical approach to the origin of basic laws of nature, using a new algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), "it is shown that certain mathematical forms of the fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms" ; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. Based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented by the corresponding quantum matrix operators) of the fundamentally derived field equations, it is concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times. On the basis of these discrete symmetries of the derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Moreover, it is shown that the (1+3)-dimensional cases of uniquely determined two classes of general covariant field equations, represent, respectively, new massive forms of the bispinor fields of spin-2, and spin-1 particles; and (1+2)-dimensional cases of these equations represent new massive forms of the bispinor fields of spin-3/2 and spin-1/2 particles, respectively. As a particular consequence, it is shown that a certain massive formalism of general relativity – with a definite form of torsion field appeared originally as the generator of gravitational field's invariant mass – is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. It has been also proved that Lagrangian densities specified for the originally derived new massive forms of the Maxwell, Yang-Mills and Dirac field equations, are also gauge invariant, where the invariant mass of each field is generated solely by the corresponding torsion field. In addition, in agreement with recent astronomical data, a new form of massive gauge boson is identified (compatible with U(1) symmetry group) with invariant mass: " m γ ≈ 4.90571×10 -50 kg ", which generated by a coupled torsion field of the background space-time geometry. Moreover, based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented basically by the corresponding quantum operators) of the fundamentally derived field equations, it has been concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times (where this conclusion, in particular, is based on the T-symmetry). It is proved that CPT is the only (unique) combination of C, P, and T symmetries that could be defined as a symmetry for interacting fields. In addition, on the basis of these discrete symmetries of derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Furthermore, it has been shown that the metric of background space-time is diagonalized for the uniquely derived fermion field equations (defined and expressed solely in (1+2)-dimensional space-time), where this property generates a certain set of additional symmetries corresponding uniquely to the "SU(2) L ⊗U(2) R " symmetry group for spin-1/2 fermion fields (representing "1+3" generations of four fermions, including a group of eight leptons and a group of eight quarks), and also the "SU(2) L ⊗U(2) R " gauge symmetry groups for spin-1 boson fields coupled to the spin-1/2 fermionic source currents. Hence, along with the known elementary particles, eight new elementary particles, including four new charge-less right-handed spin-1/2 fermions (two leptons and two quarks), a spin-3/2 fermion, and also three new spin-1 (massive) bosons are predicted axiomatically by this new mathematical approach (on a fundamental gauge-theoretic basis) . As a particular result, based on the definite matrix formalism of the uniquely derived general covariant form of Maxwell (and also Yang-Mills) field equations, it has been also concluded that magnetic monopoles could not exist in nature. Comments: 99 Pages. A summary of a submitted and accepted research project ("Foundations of Physics", "Investigation of the Origin of Space-Time", and "Ontology"), Japan, 2012 - 2015. Expanded and Presented Article's Version at "The 2016 GRavitational-Wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), Sorbonne University, 'Paris VI - UPMC, CNRS, LERU, EUA', Paris, France, 2016. 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) This article has been invited and presented at the following international conferences: -The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) -The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) -The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) -The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) -The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) -The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) -The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org) External URLs (including preprints and earlier publications of this article): https://cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, https://eprints.lib.hokudai.ac.jp/dspace/handle/2115/59279/ , http://jairo.NII.ac.jp/0003/00047402/en/, https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf, https://CORE.ac.uk/display/41880261/, http://philsci-archive.PITT.edu/11497, http://philpapers.cdp.UWO.ca/rec/zahotl/, http://www.ijqf.org/archives/3495, http://ci.NII.ac.jp/naid/120005613576, https://citeseerx.ist.PSU.edu/viewdoc/summary?doi=10.1.1.675.2202/, https://LNU.se/contentassets/1489145f113348f382202fbf0d1d4094/qb-abstracts-compiled-160613.pdf, http://mts-ncomms.Nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf , https://indico.CERN.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf .

Comments: 90 Pages. A summary of expanded version of a submitted and accepted research project (On "Foundations of Physics", and "the Origin of Space-Time"), Ramin Zahedi, Japan, 2012 - 2015. This article has been invited and presented at the following international conferences: -The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) -The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) -The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) -The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) -The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) -The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) -The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org) Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A. Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to do this work intensely as a new "unorthodox" mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research. External URLs (including preprints and earlier publications of this article): https://cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, https://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/ , http://jairo.nii.ac.jp/0003/00047402/en/, https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf, https://Eprints.lib.hokudai.ac.jp/dspace/handle/2115/60272, https://core.ac.uk/display/29500358/ , http://philsci-archive.pitt.edu/11497/, www.IJGF.org/archives/3495, http://ci.NII.ac.jp/naid/120005613576, http://philpapers.cdp.uwo.ca/rec/zahotl, https://citeseerx.ist.PSU.edu/viewdoc/summary?doi=10.1.1.675.2202, https://LNU.se/contentassets/1489145f113348f382202fbf0d1d4094/qb-abstracts-compiled-160613.pdf, https://indico.CERN.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf , http://mts-ncomms.nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf . ; International audience ; In this article, as a basic mathematical approach to the origin of the laws of nature, using a new algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), " it is shown that certain mathematical forms of the fundamental laws of nature, including laws governing the fundamental forces of nature (represented by set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms "; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to fundamental laws of nature is as follows. First based on the assumption of rationality of D-momentum, by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras) is derived. By first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford and Weyl algebras) is derived uniquely as well. Moreover, each derived field equation also includes a definite form of torsion field appeared naturally as the generator of the field's invariant mass. In addition, it is shown that (1+3)-dimensional cases of the derived two classes of field equations represent a new general covariant massive (matrix) formalism of the bispinor fields of spin-2, and spin-1 particles, respectively. These uniquely determined new bispinor fields by this axiomatic approach, in fact, represent a unique set of generalized massive forms of the laws governing the fundamental forces of nature, including the Einstein (gravitational), Maxwell (electromagnetic) and Yang-Mills (nuclear) field equations. Furthermore, it is also shown that the (1+2)-dimensional cases of derived two classes of field equations represent a new general covariant massive (matrix) formalism of the bispinor fields of spin-3/2 and spin-1/2 particles, respectively, corresponding to the Dirac and Rarita-Schwinger equations.    As a particular consequence, it is shown that a certain massive formalism of general relativity – with a definite form of torsion field appeared originally as the generator of the gravitational field's invariant mass – is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. It has been also proved that the Lagrangian densities specified for directly derived new massive forms of the Maxwell, Yang-Mills and Dirac field equations, are gauge invariant, where the invariant mass of each field is generated solely by a certain torsion field. In addition, in agreement with recent astronomical data, a new form of massive particle has been also identified (as gauge boson of the U(1) symmetry group) with invariant mass: " m γ ≈ 4.90571×10 –50 kg ", generated by a definite coupled torsion field of the background space-time geometry.    Moreover, based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented basically by the corresponding quantum operators) of the fundamentally derived field equations, it has been concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times (where this conclusion, in particular, is based on the T-symmetry). It is proved that CPT is the only (unique) combination of C, P, and T symmetries that could be defined as a symmetry for interacting fields. In addition, on the basis of these discrete symmetries of derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Furthermore, it has been shown that the metric of background space-time is diagonalized for the uniquely derived fermion field equations (defined and expressed solely in (1+2)-dimensional space-time), where this property generates a certain set of additional symmetries corresponding uniquely to the SU(2) L ⊗U(2) R symmetry group for spin-1/2 fermion fields (representing "1+3" generations of four fermions, including a group of eight leptons and a group of eight quarks), and also the SU(2) L ⊗U(2) R and SU(3) gauge symmetry groups for spin-1 boson fields coupled to the spin-1/2 fermionic source currents. Hence, along with the known elementary particles, eight new elementary particles, including four new charge-less right-handed spin-1/2 fermions (two leptons and two quarks, where the predicted two quarks "z u and z d ", specifically emerged in two subgroups with ordinary anti-quarks such that: (s̄, ū, b̄, z u ) and (c̄, d̄, t̄, z d ); there are also a similar group representation for two predicted new leptons: (ν̄ μ , e + , ν̄ τ , z e ) and (μ + , ν̄ e , τ + , z n )), a spin-3/2 fermion, and also three new spin-1 (massive) bosons (represented by W' + , W' – , Z', with properties similar to ordinary (massive) bosons W – , W + , Z, where in particular the new boson Z' is the complementary right-handed particle of ordinary Z boson) are predicted uniquely by this new axiomatic mathematical formalism. As a particular result, based on the definite matrix formalism of the derived general covariant Maxwell (and Yang-Mills) field equations, it has been also concluded that magnetic monopoles could not exist in nature. Comments: 90 Pages. A summary of expanded version of a submitted and accepted research project (On "Foundations of Physics", and "the Origin of Space-Time"), Ramin Zahedi, Japan, 2012 - 2015. This article has been invited and presented at the following international conferences: -The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) -The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) -The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) -The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) -The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) -The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) -The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org) Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A. Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to do this work intensely as a new "unorthodox" mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research. External URLs (including preprints and earlier publications of this article): https://cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, https://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/ , http://jairo.NII.ac.jp/0003/00047402/en/, https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf, https://CORE.ac.uk/display/29500358/ , http://philsci-archive.PITT.edu/11497/, www.IJGF.org/archives/3495, http://ci.NII.ac.jp/naid/120005613576, http://philpapers.cdp.UWO.ca/rec/zahotl, https://citeseerx.ist.PSU.edu/viewdoc/summary?doi=10.1.1.675.2202, https://LNU.se/contentassets/1489145f113348f382202fbf0d1d4094/qb-abstracts-compiled-160613.pdf, http://mts-ncomms.nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf , https://indico.CERN.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf .

Comments: 90 Pages. A summary of expanded version of a submitted and accepted research project (On "Foundations of Physics", and "the Origin of Space-Time"), Ramin Zahedi, Japan, 2012 - 2015. This article has been invited and presented at the following international conferences: -The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) -The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) -The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) -The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) -The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) -The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) -The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org) Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A. Shelepin (Russia), Prof. ...

Comments: 90 Pages. A summary of expanded version of a submitted and accepted research project (On "Foundations of Physics", and "the Origin of Space-Time"), Ramin Zahedi, Japan, 2012 - 2015. This article has been invited and presented at the following international conferences: -The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) -The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) -The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) -The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) -The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) -The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) -The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org) Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A. Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to do this work intensely as a new "unorthodox" mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research. External URLs (including preprints and earlier publications of this article): https://cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, https://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/ , http://jairo.nii.ac.jp/0003/00047402/en/, https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf, https://Eprints.lib.hokudai.ac.jp/dspace/handle/2115/60272, https://core.ac.uk/display/29500358/ , http://philsci-archive.pitt.edu/11497/, www.IJGF.org/archives/3495, http://ci.NII.ac.jp/naid/120005613576, http://philpapers.cdp.uwo.ca/rec/zahotl, https://citeseerx.ist.PSU.edu/viewdoc/summary?doi=10.1.1.675.2202, https://LNU.se/contentassets/1489145f113348f382202fbf0d1d4094/qb-abstracts-compiled-160613.pdf, https://indico.CERN.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf , http://mts-ncomms.nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf . ; International audience ; In this article, as a basic mathematical approach to the origin of the laws of nature, using a new algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), " it is shown that certain mathematical forms of the fundamental laws of nature, including laws governing the fundamental forces of nature (represented by set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms "; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to fundamental laws of nature is as follows. First based on the assumption of rationality of D-momentum, by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras) is derived. By first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford and Weyl algebras) is derived uniquely as well. Moreover, each derived field equation also includes a definite form of torsion field appeared naturally as the generator of the field's invariant mass. In addition, it is shown that (1+3)-dimensional cases of the derived two classes of field equations represent a new general covariant massive (matrix) formalism of the bispinor fields of spin-2, and spin-1 particles, respectively. These uniquely determined new bispinor fields by this axiomatic approach, in fact, represent a unique set of generalized massive forms of the laws governing the fundamental forces of nature, including the Einstein (gravitational), Maxwell (electromagnetic) and Yang-Mills (nuclear) field equations. Furthermore, it is also shown that the (1+2)-dimensional cases of derived two classes of field equations represent a new general covariant massive (matrix) formalism of the bispinor fields of spin-3/2 and spin-1/2 particles, respectively, corresponding to the Dirac and Rarita-Schwinger equations.    As a particular consequence, it is shown that a certain massive formalism of general relativity – with a definite form of torsion field appeared originally as the generator of the gravitational field's invariant mass – is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. It has been also proved that the Lagrangian densities specified for directly derived new massive forms of the Maxwell, Yang-Mills and Dirac field equations, are gauge invariant, where the invariant mass of each field is generated solely by a certain torsion field. In addition, in agreement with recent astronomical data, a new form of massive particle has been also identified (as gauge boson of the U(1) symmetry group) with invariant mass: " m γ ≈ 4.90571×10 –50 kg ", generated by a definite coupled torsion field of the background space-time geometry.    Moreover, based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented basically by the corresponding quantum operators) of the fundamentally derived field equations, it has been concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times (where this conclusion, in particular, is based on the T-symmetry). It is proved that CPT is the only (unique) combination of C, P, and T symmetries that could be defined as a symmetry for interacting fields. In addition, on the basis of these discrete symmetries of derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Furthermore, it has been shown that the metric of background space-time is diagonalized for the uniquely derived fermion field equations (defined and expressed solely in (1+2)-dimensional space-time), where this property generates a certain set of additional symmetries corresponding uniquely to the SU(2) L ⊗U(2) R symmetry group for spin-1/2 fermion fields (representing "1+3" generations of four fermions, including a group of eight leptons and a group of eight quarks), and also the SU(2) L ⊗U(2) R and SU(3) gauge symmetry groups for spin-1 boson fields coupled to the spin-1/2 fermionic source currents. Hence, along with the known elementary particles, eight new elementary particles, including four new charge-less right-handed spin-1/2 fermions (two leptons and two quarks, where the predicted two quarks "z u and z d ", specifically emerged in two subgroups with ordinary anti-quarks such that: (s̄, ū, b̄, z u ) and (c̄, d̄, t̄, z d ); there are also a similar group representation for two predicted new leptons: (ν̄ μ , e + , ν̄ τ , z e ) and (μ + , ν̄ e , τ + , z n )), a spin-3/2 fermion, and also three new spin-1 (massive) bosons (represented by W' + , W' – , Z', with properties similar to ordinary (massive) bosons W – , W + , Z, where in particular the new boson Z' is the complementary right-handed particle of ordinary Z boson) are predicted uniquely by this new axiomatic mathematical formalism. As a particular result, based on the definite matrix formalism of the derived general covariant Maxwell (and Yang-Mills) field equations, it has been also concluded that magnetic monopoles could not exist in nature. Comments: 90 Pages. A summary of expanded version of a submitted and accepted research project (On "Foundations of Physics", and "the Origin of Space-Time"), Ramin Zahedi, Japan, 2012 - 2015. This article has been invited and presented at the following international conferences: -The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) -The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) -The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) -The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) -The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) -The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) -The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org) Acknowledgements: Special thanks are extended to Prof. and Academician Vitaly L. Ginzburg (Russia), Prof. and Academician Dmitry V. Shirkov (Russia), Prof. Leonid A. Shelepin (Russia), Prof. Vladimir Ya. Fainberg (Russia), Prof. Wolfgang Rindler (USA), Prof. Roman W. Jackiw (USA), Prof. Roger Penrose (UK), Prof. Steven Weinberg (USA), Prof. Ezra T. Newman (USA), Prof. Graham Jameson (UK), Prof. Sergey A. Reshetnjak (Russia), Prof. Sir Michael Atiyah (UK) (who, in particular, kindly encouraged me to do this work intensely as a new "unorthodox" mathematical approach to fundamental physics), and many others for their support and valuable guidance during my studies and research. External URLs (including preprints and earlier publications of this article): https://cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, https://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/ , http://jairo.NII.ac.jp/0003/00047402/en/, https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf, https://CORE.ac.uk/display/29500358/ , http://philsci-archive.PITT.edu/11497/, www.IJGF.org/archives/3495, http://ci.NII.ac.jp/naid/120005613576, http://philpapers.cdp.UWO.ca/rec/zahotl, https://citeseerx.ist.PSU.edu/viewdoc/summary?doi=10.1.1.675.2202, https://LNU.se/contentassets/1489145f113348f382202fbf0d1d4094/qb-abstracts-compiled-160613.pdf, http://mts-ncomms.nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf , https://indico.CERN.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf .

Comments: 99 Pages. Expanded and Presented Article's Version at "The 2016 GRavitational-Wave Astronomy International Conference in Paris, Institute d'Astrophysique de Paris (IAP), Sorbonne University, 'Paris VI - UPMC, CNRS, LERU, EUA', Paris, France (2016). 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,' 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) ; International audience ; In Part I (pp. 1-10) of this article, I provide a general analysis of a number of current discontinuous approaches to fundamental physics. In Part II (the main part, pp. 11-99, Ref. [37]), as a new mathematical approach to the origin of basic laws of nature, using a new algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), "it is shown that certain mathematical forms of the fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms" ; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. Based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented by the corresponding quantum matrix operators) of the fundamentally derived field equations, it is concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times. On the basis of these discrete symmetries of the derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Moreover, it is shown that the (1+3)-dimensional cases of uniquely determined two classes of general covariant field equations, represent, respectively, new ...