The $q$-deformed Bogoliubov transformations

TL;DR

This paper introduces a novel q-deformation of Bogoliubov transformations using algebraic structures, with potential applications in Quantum Field Theory and a Hopf algebra framework at roots of unity.

Contribution

It presents a new algebraic approach to q-deformed Bogoliubov transformations, including a Hopf structure at roots of unity, expanding theoretical tools in quantum algebra.

Findings

Constructed a q-deformation of nonlinear Bogoliubov transformations

Developed a general framework applicable in Quantum Field Theory

Introduced a Hopf algebra structure at roots of unity

Abstract

An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Moreover we give a general result which can be applied in Quantum Field Theory. Finally, we introduce a Hopf structure when q is a root of unity.