Unified Gauge-Geometry Symmetry for Equilibrium Statistical Mechanics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908928234749952 |
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| author | Pham-Van, Hai |
| author_facet | Pham-Van, Hai |
| contents | We present a symmetry-based framework for equilibrium statistical mechanics that formulates a single Lie group combining conventional spacetime symmetries with a recently identified phase-space gauge-shifting invariance [Muller et al., Phys. Rev. Lett. 133, 217101 (2024)]. Using Noether's theorem, we obtain a set of general Ward identities together with previously unexplored cross-relations arising from the noncommutation of different symmetry generators. The approach extends standard many-body symmetries, such as translations, rotations, Galilean boosts, dilations, and particle exchange, by incorporating an internal gauge-shift symmetry within a unified group structure. The resulting Lie algebra suggests a hierarchy of exact identities that encompass established sum rules and indicate possible cross-coupling relations between distinct response and correlation functions. We also identify a Wigner-Eckart-Ward reduction that simplifies tensor-hyperforce correlators to two scalar radial spectra in isotropic fluids, and we outline an equivariant gauge-constrained DFT formulation whose Euler-Lagrange equations are constructed to satisfy the corresponding Ward and cross-Ward constraints. This framework provides a consistent organizational basis for phenomena in liquids, mixtures, and interfaces, and may offer a symmetry-based perspective connecting structure, mechanics, and dynamics in many-body systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unified Gauge-Geometry Symmetry for Equilibrium Statistical Mechanics Pham-Van, Hai Statistical Mechanics Soft Condensed Matter We present a symmetry-based framework for equilibrium statistical mechanics that formulates a single Lie group combining conventional spacetime symmetries with a recently identified phase-space gauge-shifting invariance [Muller et al., Phys. Rev. Lett. 133, 217101 (2024)]. Using Noether's theorem, we obtain a set of general Ward identities together with previously unexplored cross-relations arising from the noncommutation of different symmetry generators. The approach extends standard many-body symmetries, such as translations, rotations, Galilean boosts, dilations, and particle exchange, by incorporating an internal gauge-shift symmetry within a unified group structure. The resulting Lie algebra suggests a hierarchy of exact identities that encompass established sum rules and indicate possible cross-coupling relations between distinct response and correlation functions. We also identify a Wigner-Eckart-Ward reduction that simplifies tensor-hyperforce correlators to two scalar radial spectra in isotropic fluids, and we outline an equivariant gauge-constrained DFT formulation whose Euler-Lagrange equations are constructed to satisfy the corresponding Ward and cross-Ward constraints. This framework provides a consistent organizational basis for phenomena in liquids, mixtures, and interfaces, and may offer a symmetry-based perspective connecting structure, mechanics, and dynamics in many-body systems. |
| title | Unified Gauge-Geometry Symmetry for Equilibrium Statistical Mechanics |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2604.00354 |