How to Solve Quantum Nonlinear Abelian Gauge Theory in Two Dimension in the Heisenberg Picture

TL;DR

This paper introduces a new operator formalism method to exactly solve two-dimensional quantum nonlinear abelian gauge theories, potentially aiding the analysis of more complex theories like gravity.

Contribution

It extends the Abe and Nakanishi operator formalism to a broader class of quantum field theories and provides exact solutions in the Heisenberg picture.

Findings

Exact solutions for the quantum nonlinear abelian gauge theory in 2D

Extension of soluble models to wider quantum field theories

Potential insights into gravitational and non-polynomial field theories

Abstract

The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear abelian gauge theory in two dimension. The soluble models in this method are extended to wider class of quantum field theories. We obtain the exact solution in the canonical-quantization operator formalism in the Heisenberg picture. So this analysis might shed some light on the analysis of gravitational theory and non-polynomial field theories.