https://doi.org/10.1140/epjp/s13360-024-05750-7
Tutorial
Gauge symmetries for the classification of the physical states
Dipartimento di Fisica, Università di Pisa, Pisa, Italy
Received:
11
July
2024
Accepted:
15
October
2024
Published online:
3
November
2024
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the substantially different role of local gauge symmetries. In the latter case, a deterministic time evolution of the local field algebra, necessary for field quantization, requires a reduction of the full local gauge group 
to a residual local subgroup 
satisfying suitable conditions. A non-trivial residual local gauge group allows for the use of a local field algebra, otherwise precluded if is reduced to the identity. Moreover, in the non-abelian case a residual allows to exploit its topology, which provides the (gauge invariant) topological invariants which classify the vacuum structure with important physical effects. Furthermore, it provides a general mechanism of spontaneous symmetry breaking without Goldstone bosons.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
