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

• Published in: Annals of physics Vol. 380; pp. 12 - 22
• Main Authors: Mendes, Albert C.R., Takakura, Flavio I., Abreu, Everton M.C., Neto, Jorge Ananias
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01-05-2017
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Compressible fluid; Electromagnetic background; ELECTROMAGNETIC FIELDS; HAMILTONIANS; LAGRANGIAN FUNCTION; MAXWELL EQUATIONS; PARTITION FUNCTIONS; PATH INTEGRALS; Stefan–Boltzmann law; Compressible fluid; Electromagnetic background; Stefan–Boltzmann law
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2017.02.017

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 were 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.
•Higher-derivative Lagrangian for a charged fluid.•Electromagnetic coupling and Dirac’s constraint analysis.•Partition function through path integral formalism.•Stefan–Boltzmann-kind law through the partition function.