Local-equilibrium density operators built only from genuine conserved currents are invariant under pseudo-gauge and improvement transformations of the energy-momentum and spin tensors.
Hongo,Path-integral formula for local thermal equilibrium,Annals Phys.383(2017) 1 [1611.07074]
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abstract
We develop a complete path-integral formulation of relativistic quantum fields in local thermal equilibrium, which brings about the emergence of thermally induced curved spacetime. The resulting action is shown to have full diffeomorphism invariance and gauge invariance in thermal spacetime with imaginary-time independent backgrounds. This leads to the notable symmetry properties of emergent thermal spacetime: Kaluza-Klein gauge symmetry, spatial diffeomorphism symmetry, and gauge symmetry. A thermodynamic potential in local thermal equilibrium, or the so-called Masseiu-Planck functional, is identified as a generating functional for conserved currents such as the energy-momentum tensor and the electric current.
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2026 2representative citing papers
Unified computation of chiral anomalous transport effects including mass corrections from integrating out a Dirac fermion in EFT at finite temperature, showing physical currents differ from Chern-Simons terms.
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A symmetry-based resolution of pseudo-gauge ambiguities in local equilibrium
Local-equilibrium density operators built only from genuine conserved currents are invariant under pseudo-gauge and improvement transformations of the energy-momentum and spin tensors.
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Anomalous Transport from Effective Field Theory
Unified computation of chiral anomalous transport effects including mass corrections from integrating out a Dirac fermion in EFT at finite temperature, showing physical currents differ from Chern-Simons terms.