Bosonization of Thirring Model in Arbitrary Dimension

Abstract

We propose to use a novel master Lagrangian for performing the bosonization of the $D$-dimensional massive Thirring model in $D=d+1\ge 2$ dimensions. It is shown that our master Lagrangian is able to relate the previous interpolating Lagrangians each other which have been recently used to show the equivalence of the massive Thirring model in (2+1) dimensions with the Maxwell-Chern-Simons theory. Starting from the phase-space path integral representation of the master Lagrangian, we give an alternative proof for this equivalence up to the next-to-leading order in the expansion of the inverse fermion mass. Moreover, in (3+1)-dimensional case, the bosonized theory is shown to be equivalent to the massive antisymmetric tensor gauge theory. As a byproduct, we reproduce the well-known result on bosonization of the (1+1)-dimensional Thirring model following the same strategy. Finally a possibility of extending our strategy to the non-Abelian case is also discussed.

26 pages, latex, ( a few references added)

References in corpus (3)

• On the Equivalence of the Maxwell-Chern-Simons Theory and a Self-Dual Model
• Thirring Model as a Gauge Theory
• Thirring Model as a Gauge Theory

Cited by in corpus (9)

• Bosonisation and Duality Symmetry in the Soldering Formalism
• Explicit Bosonization of the Massive Thirring Model in 3+1 Dimensions
• Non abelian bosonisation in three dimensional field theory
• Different Approaches for Bosonization in Higher Dimensions
• Duality between 3D Massive Thirring and Maxwell Chern-Simons models from 2D bosonization
• Duality and an Operator Realization for the Fermi-Bose Transmutation in 3+1 Dimensions
• Bosonization and Duality in Arbitrary Dimensions: New Results
• Duality and Topological Mass Generation in Diverse Dimensions
• Nonperturbative Aspects of the two-dimensional Massive Gauged Thirring Model