[Paper Review] Interacting Gauge-Fluid system

Rabin Banerjee, Subir Ghosh+1 more|arXiv (Cornell University)|Apr 22, 2016

Cosmology and Gravitation Theories8 references3 citations

TL;DR

This paper develops a relativistic gauge-fluid model coupling a non-isentropic fluid to a dynamical $U(1)$ gauge field, comparing canonical and symmetric energy-momentum tensors. It establishes equivalence of spacetime generator algebras modulo Gauss constraint and confirms the Schwinger condition, with novel insights in lightcone formalism.

ABSTRACT

A gauge-fluid relativistic model where a non-isentropic fluid is coupled to a dynamical Maxwell ($U(1)$) gauge field, has been studied. We have examined in detail the structures of energy momentum 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.

Motivation & Objective

• To formulate a consistent relativistic coupling between a non-isentropic fluid and a dynamical Maxwell gauge field.
• To compare the canonical (Noether) and symmetric definitions of the energy-momentum tensor in this system.
• To investigate the physical equivalence of spacetime symmetry generators derived from both energy-momentum definitions.
• To verify the validity of the Schwinger condition in the context of this gauge-fluid model.
• To explore the model’s structure using the lightcone formalism and uncover new dynamical features.

Proposed method

• Derives the energy-momentum tensor using both the canonical (Noether) and symmetric definitions in the equal-time formalism.
• Compares the generators of spacetime transformations (Poincaré algebra) from both energy-momentum definitions.
• Demonstrates that the two generator sets agree modulo the Gauss constraint, relying on the dynamical nature of the gauge field.
• Explicitly verifies the Schwinger condition using the derived tensor structures and constraints.
• Applies the lightcone formalism to analyze the model, revealing non-trivial dynamical and algebraic features.
• Analyzes the role of constraints, particularly the Gauss law, in ensuring physical equivalence between the two tensor definitions.

Experimental results

Research questions

• RQ1 To what extent do the canonical and symmetric energy-momentum tensors yield equivalent spacetime symmetry generators in a gauge-fluid system?
• RQ2 How does the dynamical nature of the gauge field enable equivalence between the two energy-momentum definitions?
• RQ3 Does the Schwinger condition hold in a relativistic fluid coupled to a dynamical $U(1)$ gauge field?
• RQ4 What new structural features emerge when the gauge-fluid model is analyzed in the lightcone formalism?
• RQ5 How do constraints, especially the Gauss constraint, affect the physical equivalence of the two energy-momentum definitions?

Key findings

• The generators of spacetime transformations derived from the canonical and symmetric energy-momentum tensors are physically equivalent modulo the Gauss constraint.
• This physical equivalence is contingent on the gauge field being dynamical, as static or non-dynamical fields would break the equivalence.
• The Schwinger condition is explicitly verified in the model, confirming consistency with quantum field theory requirements.
• The lightcone formalism reveals non-trivial algebraic and dynamical structures not apparent in the equal-time formulation.
• The analysis confirms that the physical sector of the theory is consistently described by both energy-momentum tensor definitions when constraints are properly enforced.
• The model demonstrates that the symmetric energy-momentum tensor is physically viable and consistent with the canonical one in the presence of dynamical gauge fields.