Quantum Electrodynamics in Two-Dimensions at Finite Temperature. Thermofield Bosonization Approach

TL;DR

This paper extends the analysis of the Schwinger model to finite temperatures using thermofield bosonization, revealing a rich structure of thermal vacuum states and providing explicit formulas for the chiral condensate at any temperature.

Contribution

It generalizes the operator solution of the Schwinger model to finite temperature within the thermofield bosonization framework, uncovering multiple thermal vacuum states and deriving the temperature dependence of the chiral condensate.

Findings

Existence of infinitely many thermal vacuum states with same charge and chirality.

Explicit expression for the chiral condensate at arbitrary temperature.

High-temperature behavior of the chiral condensate derived.

Abstract

The Schwinger model at finite temperature is analyzed using the Thermofield Dynamics formalism. The operator solution due to Lowenstein and Swieca is generalized to the case of finite temperature within the thermofield bosonization approach. The general properties of the statistical-mechanical ensemble averages of observables in the Hilbert subspace of gauge invariant thermal states are discussed. The bare charge and chirality of the Fermi thermofields are screened, giving rise to an infinite number of mutually orthogonal thermal ground states. One consequence of the bare charge and chirality selection rule at finite temperature is that there are innumerably many thermal vacuum states with the same total charge and chirality of the doubled system. The fermion charge and chirality selection rules at finite temperature turn out to imply the existence of a family of thermal theta vacua states parametrized with the same number of parameters as in zero temperature case. We compute the thermal theta-vacuum expectation value of the mass operator and show that the analytic expression of the chiral condensate for any temperature is easily obtained within this approach, as well as, the corresponding high-temperature behavior.