Symmetries and invariances in classical physics

Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic

Symmetries in Physics: Philosophical Reflections

This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern physics. Then, in section 2, we mention the different varieties of symmetry that fall under this general umbrella, outlining the ways in which they were introduced into physics. We also distinguish between two different uses of symmetry: symmetry principles versus symmetry arguments. In section 3 we make some remarks of a general nature concerning the status and significance of symmetries in physics. Finally, in section 4, we outline the structure of the book and the contents of each part.Comment: 16 pages. To appear in K. Brading and E. Castellani (eds.), "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 200

Hopf Algebras in General and in Combinatorial Physics: a practical introduction

This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced

New Physics in Bs -> J/psi phi: a General Analysis

Recently, the CDF and D0 collaborations measured indirect CP violation in Bs -> J/psi phi and found a hint of a signal. If taken at face value, this can be interpreted as a nonzero phase of Bs-Bsbar mixing (beta_s), in disagreement with the standard model, which predicts that beta_s ~= 0. In this paper, we argue that this analysis may be incomplete. In particular, there can be new physics (NP) in the bbar -> sbar c cbar decay. If so, the value of beta_s is different than for the case in which NP is assumed to be present only in the mixing. We have examined several models of NP and found that, indeed, there can be significant contributions to the decay. These effects are consistent with measurements in B -> J/psi K* and Bd -> J/psi Ks. Due to the NP in the decay, polarization-dependent indirect CP asymmetries and triple-product asymmetries are predicted in Bs -> J/psi phi.Comment: 28 pages, JHEP, no figures. Considerable changes made. Abstract and main text of paper modified to alter presentation. Appendix added. References added. Conclusions unchanged