Hidden symmetries in quantum field theories from extended complex numbers

TL;DR

This paper extends the sine-Gordon quantum field theory into n-dimensional extended complex numbers, revealing hidden symmetries and constructing non-local conserved charges, thus providing a new algebraic non-perturbative framework.

Contribution

It introduces an algebraic extension of sine-Gordon theory using extended complex numbers, enabling a unified non-perturbative description of related quantum field theories.

Findings

Constructed non-local conserved charges in extended complex number framework

Reproduced known results for affine Toda field theories

Unified description of dual models within the extended algebraic formalism

Abstract

The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A whole set of non-local conserved charges is constructed and studied in this framework. Thereby, an algebraic non-perturbative description is possible for this n-1 parameters family of quantum field theories. Known results are obtained for specific values of the parameters, especially in relation to affine Toda field theories. Different (dual)-models can then be described in this formalism.