arXiv:1006.1580v1 [hep-th] 8 Jun 2010 Nonperturbative functional quantization and strong coupling isomorphisms of the gauged Thirring model R. Bufalo 1∗ , R. Casana 2 † and B.M. Pimentel 1 ‡ 1 Instituto de F´ ısica Te´ orica (IFT/UNESP), UNESP - S˜ ao Paulo State University Rua Dr. Bento Teobaldo Ferraz 271, Bloco II Barra Funda, CEP 01140-070,S˜ ao Paulo, SP, Brazil 2 Departamento de F´ ısica, Universidade Federal do Maranh˜ ao (UFMA), Campus Universit´ ario do Bacanga, CEP 65085-580, S˜ ao Lu´ ıs - MA, Brasil. Abstract We have performed a nonperturbative quantization of the two-dimensional gauged Thirring model by using the path-integral approach. First, we have studied the constraint structure via the Dirac’s formalism for constrained systems and by using the Faddeev-Senjanovic method we have calculated the vacuum–vacuum transition amplitude, then have computed the correlation functions in a nonperturbative framework, and the Ward-Takahashi identities of model as well. Afterwards, we have established at quantum level the isomorphisms between gauged Thirring model with the Schwinger and Thirring models by analyzing the respective Green’s functions in the strong limit of the coupling constants g and e, respectively. A special attention is necessary to perform the quantum analysis in the limit e →∞. 1 Introduction In general, none of the well-known quantization procedures allow to solve any gauge theory model exactly in (3+1)− dimensions. However, many interesting features appear in theoretical field models when they are analyzed them in low-dimensional space-times [1]. Thus, some models like quantum electrodynamics and fermionic quartic interactions become exactly solvable in (1+1)−dimensions. In that way, in the past few years, the interest has grown in exactly solvable low-dimensional quantum field models, for example in (1+1)- and (2+1)-dimensions, due to their applicability in Condensate Matter Physics, via the formalism named as the Finite Temperature Field Theory [2]. The two-dimensional field theories have been widely explored to test various relevant phenomena in more realistic models, such as dynamical mass generation, asymptotic freedom and confinement. The research of solvable models in quantum field theory has its beginning with the proposals of W. Thirring and J. Schwinger. For example, Schwinger [3] has shown two important features, that it is not necessary a massless gauge field to preserve the local gauge symmetry and that the fermionic field is confined, in total analogy with the quark confinement phenomenon happening in quantum chromodynamics (QCD 4 ). The Thirring model [4] (TM) describes a self-interaction of massless Dirac’s fermion fields in (1+1)−dimensions and some exact solutions of model were carried out by B. Klaiber [5] and by N. * rbufalo@ift.unesp.br † casana@ufma.br ‡ pimentel@ift.unesp.br