Finite temperature Thirring model: from linearization through canonical transformations to correct normal form of thermofield solution

TL;DR

This paper demonstrates the exact solvability of the finite temperature massless Thirring model through canonical transformations, revealing hidden linearizability, correct renormalization, and new insights into thermofield representations and superselection rules.

Contribution

It introduces a novel approach to solve the finite temperature Thirring model using canonical transformations and generalizes thermofield methods for better understanding of thermal quantum fields.

Findings

Exact solvability of finite temperature Thirring model established.

Normal forms of thermofield solutions connected via conformal shifts.

New sources of superselection rules and generalized conjugation rules identified.

Abstract

It is shown that exact solvability of the finite temperature massless Thirring model, as well as of its zero temperature case, in canonical quantization scheme originates from the intrinsic hidden exact linearizability of Heisenberg equations by means of dynamical mapping onto the Schr\"odinger physical fields. The normal forms of different one- and two- parametric (thermo) field's solutions are obtained. They are connected with each other by making use of generalized conformal shift transformations. The sequential use of bosonic canonical transformations provides a correct renormalization, anticommutation and symmetry properties of these solutions. The dynamical role of inequivalent representations of 1+1-D free massless Dirac fields, that are induced by inequivalent representations of 1+1-D free massless (pseudo) scalar field, and the appearance of Schwinger terms are elucidated. The inequivalent vacuum is established as coherent state for SU(1,1) group. A new alternative sources of superselection rules are shown. A generalization of Ojima tilde conjugation rules is suggested, which reveals the properties of coherent state for SU(2) group for the fermionic thermal vacuum state and is useful for the thermofield bosonization. The notions of "hot" and "cold" thermofields are introduced to distinguish different thermofield representations giving the correct normal form of thermofield solution. The weak sense of definition of zero and finite temperature operator bosonization rules in the framework of thermofield dynamics is demonstrated.