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URN to cite this document: urn:nbn:de:bvb:703-epub-9200-6
Title data
Müller, Johanna ; Sammüller, Florian ; Schmidt, Matthias:
Why gauge invariance applies to statistical mechanics.
In: Journal of Physics A: Mathematical and Theoretical.
Vol. 58
(2025)
.
- 125003.
ISSN 1751-8121
DOI der Verlagsversion: https://doi.org/10.1088/1751-8121/adbfe6
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Project information
| Project title: |
Project's official title Project's id Neuronale Funktionaltheorie für inhomogene weiche Materie 551294732 Open Access Publizieren No information |
|---|---|
| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems (Müller et al 2024 Phys. Rev. Lett. 133 217101). The gauge transformation is a non-commutative shifting operation on phase space that keeps the differential phase space volume element and hence the Gibbs integration measure conserved. When thermally averaged any observable is an invariant, including thermodynamic and structural quantities. Shifting transformations are canonical in the sense of classical mechanics. They also form an infinite-dimensional group with generators of infinitesimal transformations that build a non-commutative Lie algebra. We lay out the connections with the underlying geometry of coordinate displacement and with Noether’s theorem. Spatial localization of the shifting yields differential operators that satisfy commutator relationships, which we describe both in purely configurational and in full phase space setups. Standard operator calculus yields corresponding equilibrium hyperforce correlation sum rules for general observables and order parameters. Using Monte Carlos simulations we demonstrate explicitly the gauge invariance for finite shifting. We argue in favor of using the gauge invariance as a statistical mechanical construction principle for obtaining exact results and for formulating smart sampling algorithms.
Further data
| Item Type: | Article in a journal |
|---|---|
| DDC Subjects: | 500 Science > 530 Physics |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II > Chair Theoretical Physics II - Univ.-Prof. Dr. Matthias Schmidt Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-9200-6 |
| Date Deposited: | 15 May 2026 10:19 |
| Last Modified: | 15 May 2026 10:20 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/9200 |
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