The Schwinger Model on a circle: relation between Path Integral and Hamiltonian approaches

TL;DR

This paper provides an exact Hamiltonian solution of the massless Schwinger model on a circle, explicitly constructs physical states, and compares Hamiltonian and Path Integral approaches through correlation functions.

Contribution

It establishes a detailed connection between Hamiltonian and Path Integral formalisms for the Schwinger model on a circle, including explicit state construction and nonperturbative analysis.

Findings

Explicit physical states constructed in Hamiltonian formalism

Correlation functions match between Hamiltonian and Path Integral methods after analytical continuation

Nonperturbative vacua and spectral flow analyzed in the model

Abstract

We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean Path Integral formalism obtained before.