Suchergebnisse

With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural way to justify and extend the classical approximation. A simple proposal is presented that can allow us to give systematic quantum corrections to the evolution of expectation values and/or an estimate of the errors committed when using the classical approximation. The method is applied to the case of a few degrees of freedom and compared with other methods and with the exact quantum results. An analysis of the dependence of the numerical effort involved as a function of the number of variables is given, which allows us to be optimistic about its applicability in a quantum field theoretical context ; We acknowledge financial support from the MCINN Grants No. FPA2009-08785 and No. FPA2009-09017, the Comunidad Autónoma de Madrid under the Program No. HEPHACOS S2009/ESP- 1473, and the European Union under Grant Agreement No. PITN-GA-2009-238353 (ITN STRONGnet). The authors participate in the Consolider-Ingenio 2010 CPAN (CSD2007-00042). We acknowledge the use of the IFT clusters for part of our numerical results

Journal of High Energy Physics 2011.07 (2011): 034 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA) ; We present a detailed study of a filtering method based upon Dirac quasi-zero-modes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of motion. On the other hand, it is very effective in reducing the short-wavelength stochastic noise present in Monte-Carlo generated configurations. After testing the performance of the method in various situations, we apply it successfully to study the effect of Monte-Carlo dynamics on topological structures like instantons ; We acknowledge financial support from the MCINN grants FPA2009-08785 and FPA2009-09017, the Comunidad Autónoma de Madrid under the program HEPHACOS S2009/ESP-1473, and the European Union under Grant Agreement number PITN-GA-2009-238353 (ITN STRONGnet). The authors participate in the Consolider-Ingenio 2010 CPAN (CSD2007-00042). We acknowledge the use of the IFT clusters for part of our numerical results

Journal of High Energy Physics 2015.1 (2015): 038 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA) ; We measure the running of the SU(∞) 't Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU(N) gauge theory on a single site lattice with twisted boundary conditions. The computation relies on the conjecture that finite volume effects for SU(N) gauge theories defined on a 4-dimensional twisted torus are controlled by an effective size parameter ˜l = l√ N, with l the torus period. We set the scale for the running coupling in terms of ˜l and use the gradient flow to define a renormalized 't Hooft coupling λ(˜l). In the TEK model, this idea allows the determination of the running of the coupling through a step scaling procedure that uses the rank of the group as a size parameter. The continuum renormalized coupling constant is extracted in the zero lattice spacing limit, which in the TEK model corresponds to the large N limit taken at fixed value of λ(˜l). The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at N = ∞. The idea is shown to work and permits us to follow the evolution of the coupling over a wide range of scales. At weak coupling we find a remarkable agreement with the perturbative two-loop formula for the running coupling ; We acknowledge financial support from the MCINN grants FPA2009-08785, FPA2009-09017, FPA2012-31686 and FPA2012-31880, the Comunidad Autónoma de Madrid under the program HEPHACOS S2009/ESP-1473, the European Union under Grant Agreement PITN-GA-2009-238353 (ITN STRONGnet), and the Spanish MINECO's "Centro de Excelencia Severo Ochoa" Programme under grant SEV-2012-0249. M. O. is supported by the Japanese MEXT grant No 26400249