Toward Construction of Exact Operator Solution of $A_N$-Toda Field Theory

TL;DR

This paper develops a method for constructing exact operator solutions in quantum $A_N$-Toda field theory using canonical free field quantization, focusing on the Toda exponential operator related to fundamental weights.

Contribution

It introduces a novel approach to quantizing $A_N$-Toda field theory and explicitly constructs the Toda exponential operator for fundamental weights.

Findings

Successful construction of the Toda exponential operator for fundamental weights.

Advancement in quantization techniques for $A_N$-Toda field theory.

Potential applications to exact solutions in integrable quantum field theories.

Abstract

Quantum $A_N$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operator associated with the fundamental weight $\lambda^1$ is constructed.