Q-boson coherent states and para-Grassmann variables for multi-particle states

TL;DR

This paper develops a framework of coherent states and Grassmann calculus for multi-mode q-boson systems, enabling advanced symbolic and trace calculations relevant to quantum statistical mechanics.

Contribution

It introduces generalized Grassmann variables and coherent states for multiple q-boson modes, expanding the mathematical tools for quantum many-body systems.

Findings

Resolution of unity via generalized Berezin integrals

Formulas for operator traces in q-boson systems

Discussion of the thermodynamic partition function

Abstract

We describe coherent states and associated generalized Grassmann variables for a system of $m$ independent $q$-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus. Formulae for operator traces are given and the thermodynamic partition function for a system of $q$-boson oscillators is discussed.