Strong coupling limits and quantum isomorphisms of the gauged Thirring model

TL;DR

This paper investigates the quantum equivalence of the gauged Thirring model with Schwinger and Thirring models in strong coupling limits using nonperturbative path-integral methods and Green's functions analysis.

Contribution

It establishes quantum isomorphisms between the gauged Thirring model and both Schwinger and Thirring models through a nonperturbative path-integral approach and Green's functions analysis.

Findings

Quantum isomorphisms are established in strong coupling limits.

Green's functions and Ward-Takahashi identities are exactly computed.

The analysis clarifies the relationship between the gauged Thirring, Schwinger, and Thirring models.

Abstract

We have studied the quantum equivalence in the respective strong coupling limits of the bidimensional gauged Thirring model with both Schwinger and Thirring models. It is achieved following a nonperturbative quantization of the gauged Thirring model into the path-integral approach. First, we have established the constraint structure via the Dirac's formalism for constrained systems and defined the correct vacuum--vacuum transition amplitude by using the Faddeev-Senjanovic method. Next, we have computed exactly the relevant Green's functions and shown the Ward-Takahashi identities. Afterwards, we have established the quantum isomorphisms between gauged Thirring model and both Schwinger and Thirring models by analyzing the respective Green's functions in the strong coupling limits, respectively. A special attention is necessary to establish the quantum isomorphism between the gauged Thirring model and the Thirring model.