On the equivalence among stress tensors in a gauge-fluid system

TL;DR

This paper demonstrates the equivalence of different stress tensor definitions in a relativistic gauge-fluid system with dynamical gauge fields, highlighting the importance of gauge dynamics in ensuring consistent physical descriptions.

Contribution

It shows the equivalence of canonical and symmetric stress tensors in a gauge-fluid model with dynamical gauge fields, emphasizing the role of gauge dynamics in this equivalence.

Findings

Equivalence of stress tensors on the physical subspace

Validation of the Schwinger condition in the model

Insights from lightcone formalism analysis

Abstract

In this paper we bring out the subtleties involved in the study of a first order relativistic field theory with auxiliary field variables playing an essential role. In particular we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a {\it dynamical} Maxwell ($U(1)$) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, {\it{ie.}} the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the spacetime transformations obtained from these two definitions agree, modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.