Comment on $q$-deformation in Second Quantization Procedure

TL;DR

This paper investigates how $q$-deformation affects the algebra of basis vectors in second quantization within 1+1 dimensional quantum field theories, ensuring field invariance under quantum group coaction.

Contribution

It introduces a deformation of the basis vector algebra in second quantization, maintaining field invariance under quantum group coaction in 1+1D quantum field theories.

Findings

Deformed algebra of basis vectors in second quantization.

Preservation of field operator invariance under quantum group coaction.

Extension of $q$-deformation concepts to 1+1D quantum field theories.

Abstract

When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under the coaction of the quantum group. In the 1+1 dimensional quantum field theories we deform the algebra of the basis vectors and study the $q$-deformation in the second quantization procedure.