Compressible Fluids with Maxwell-type equations, the minimal coupling with electromagnetic field and the Stefan-Boltzmann law

TL;DR

This paper develops a higher-derivative Lagrangian for a charged fluid coupled with electromagnetic fields, analyzes constraints, and derives a Stefan-Boltzmann law using path integral methods.

Contribution

It introduces a novel higher-derivative Lagrangian for charged fluids with electromagnetic coupling and derives a Stefan-Boltzmann law from this framework.

Findings

Derived a higher-derivative Lagrangian for charged fluids

Performed Dirac's constraints analysis and gauge fixing

Obtained a Stefan-Boltzmann type law from the partition function

Abstract

In this work we have obtained a higher-derivative Lagrangian for a charged fluid coupled with the electromagnetic fluid and the Dirac's constraints analysis was discussed. A set of first-class constraints fixed by noncovariant gauge condition was obtained. The path integral formalism was used to obtain the partition function for the corresponding higher-derivative Hamiltonian and the Faddeev-Popov ansatz was used to construct an effective Lagrangian. Through the partition function, a Stefan-Boltzmann type law was obtained.