On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

Abstract

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin-Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows to identify the topological charge in the sine-Gordon model with the fermion number.

62 pages, 3 figures,misprints are corrected, the chiral Jacobian is recalculated and a few references are added

References in corpus (1)

• On the solution of the massless Thirring model with fermion fields quantized in the chiral symmetric phase

Cited by in corpus (21)

• On the propagation of binary signals in damped mechanical systems of oscillators
• Criticality of quantum energy teleportation at phase transition points in quantum field theory
• Renormalizable parameters of the sine-Gordon model
• Minimal conductivity of rippled graphene with topological disorder
• Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?
• Massless fermions in multi-flavor QED_2
• On the applicability of the layered sine-Gordon model for Josephson-coupled high-T_c layered superconductors
• New Vacuum of Bethe Ansatz Solutions in Thirring Model
• The Effect of Interactions on the Conductance of Graphene Nanoribbons
• Exact Asymptotic Behaviour of Fermion Correlation Functions in the Massive Thirring Model
• Massless Thirring model in canonical quantization scheme
• Renormalization group analysis of the hyperbolic sine-Gordon model -- Asymptotic freedom from cosh interaction --
• Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model
• Renormalized new solutions for the massless Thirring model
• Bound State Spectrum of Massive Thirring Model in Rest Frame
• Massless Pseudoscalar Fields and Solution of the Federbush Model
• Bosonization in the path integral formulation
• Finite temperature Thirring model: from linearization through canonical transformations to correct normal form of thermofield solution
• Non-equivalence between Heisenberg XXZ spin chain and Thirring model
• Phase Structure of Compact QED from the Sine-Gordon/Massive Thirring Duality
• On the origin of superselection rules and different solutions of Thirring model