The Meaning and Facets of `Symmetry' in Physics
Domenico Giulini
Abstract
This paper is an English translation of a contribution to the latest German edition (2017) of Hermann Weyl's classic text "Symmetry", edited and annotated by Erhard Scholz, Klaus Volkert, and myself. In this contribution I discuss various physical aspects of the notion of symmetry and place them in context from the perspective of theoretical physics. In particular, a distinction is drawn between symmetries of individual configurations (solutions of equilibrium equations or equations of motion) and symmetries of the laws themselves. Likewise, a distinction is made between those operations that alter physical states and so-called gauge symmetries, which leave physical states unchanged and merely represent a redundancy in the mathematical description. Besides gauge symmetries, I comment on the connection to conservation laws, symmetry breaking, and the philosophy of space.
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