Smooth Bosonization as a Quantum Canonical Transformation

Abstract We consider a 1+1 dimensional field theory which contains both a complexfermion field and a real scalar field. We then construct a unitary operatorthat, by a similarity transformation, gives a continuum of equivalent theorieswhich smoothly interpolate between the massive Thirring model and the sine-Gordon model. This provides an implementation of smooth bosonizationproposed by Damgaard et al. as well as an example of a quantum canonicaltransformation for a quantum field theory.I. INTRODUCTION Duality, or the quantum equivalence of field theories, allows one to relate quantities inone theory, such as the particle spectrum and Green’s functions, to those of another theory.This concept is most useful when duality maps a theory with a strong coupling, in whichperturbation theory is invalid, to one with a weak coupling, in which a perturbative calcula-tion may be performed. Unfortunately, most such duality transformations are hypotheticalsince an explicit operator mapping is absent. Duality is usually demonstrated either by