The Meaning and Facets of `Symmetry' in Physics
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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BibTeX
@misc{giulini2026meaning,
title = {{The Meaning and Facets of `Symmetry' in Physics}},
author = {Domenico Giulini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12488},
eprint = {2610.12488},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12488},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Meaning and Facets of `Symmetry' in Physics
AU - Domenico Giulini
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.12488
UR - https://arxiv.org/abs/2610.12488
AB - 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.
ER -