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The most general Lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations ; This work has received funding from the Spanish Research Agency (Agencia Estatal de Investigacion) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grants agreement No 674896 and No 690575. We also have been partially supported by FPA2016-78645-P(Spain). RSG is supported by the Spanish FPU Grant No FPU16/01595

This paper points out the fundamental transformation and derivation rules concerning the Park's transforms. Using these rules the invariance of the written with the (ψ, U) set Park's equations and their non invariance with the (I, U) set are straightforwardly assessed.

Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.

Frontmatter -- Contents -- Preface -- Acknowledgments -- Introduction -- 1 Scientific Representation -- 2 Models, Symmetry, and Convention -- 3 A New Appraisal of Symmetry -- 4 Simultaneity and Convention -- 5 Objectivity in the Twin Paradox -- 6 Localization in Quantum Theory -- Conclusion -- Appendix A -- Appendix B -- Notes -- Index

AbstractAn abstract game satisfies Dominance Invariance if the indirect and the direct dominance relations, or myopic and farsighted dominance, are equivalent. Mauleon et al. (Int J Game Theory 43(4):925–943, 2014) study Dominance Invariance as an attractive condition that eliminates the differences between a farsighted solution concept and its myopic counterpart. We show that Dominance Invariance can also be used to eliminate the differences between various farsighted solution concepts in any abstract game. Together with an additional condition called No Infinite Chains, Dominance Invariance implies the existence and uniqueness of the farsighted stable set, its equivalence to the largest consistent set and its equivalence to the (strong) rational expectations farsighted stable set when the latter exists. This also implies that both the farsighted stable set and the largest consistent set do not suffer from the problem of maximality under these conditions.

AbstractThis study addresses the problem of Arrovian preference aggregation. Social rationality plays a crucial role in the standard Arrovian framework. However, no assumptions on social rationality are imposed here. Social preferences are allowed to be any binary relation (possibly incomplete and intransitive). We introduce the axiom of hybrid invariance, which requires that if social preferences under two preference profiles make the same judgment, then a social preference under a "hybrid" of the two profiles must extend the original judgment in a certain way. Then, we characterize the structure of decisive coalitions under hybrid invariance.

This article examines methodological individualism in terms of the theory that invariance under intervention is the signal feature of generalizations that serve as a basis for causal explanation. This theory supports the holist contention that macro-level generalizations can explain, but it also suggests a defense of methodological individualism on the grounds that greater range of invariance under intervention entails deeper explanation. Although this individualist position is not threatened by multiple-realizability, an argument for it based on rational choice theory is called into question by experimental results concerning preference reversals.

Descriptions of social norms can be explanatory. The erotetic approach to explanation provides a useful framework. I describe one very broad kind of explanation-seeking why-question, a genus that is common to the special sciences, and argue that descriptions of norms can serve as an answer to such why-questions. I draw upon Woodward's recent discussion of the explanatory role of generalizations with a significant degree of invariance. Descriptions of norms provide what is, in effect, a generalization regarding the kind of historically contingent system— a group or society, a generalization with a significant degree of invariance.