q-Functional Wick's theorems for particles with exotic statistics

TL;DR

This paper develops a q-functional framework for quantum field theory involving particles with exotic statistics, extending Wick's theorems to these systems and enabling perturbative analysis.

Contribution

It introduces q-functional analogues of Wick's theorems for exotic particles, generalizing standard field theory methods to new quantum statistics.

Findings

Derived q-functional Wick's theorems for exotic particles.

Formulated perturbation series in q-functional quantum field theory.

Established a foundation for analyzing systems with q-particles.

Abstract

In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we prove the q-functional analogues of Hori's formulation of Wick's theorems for the different ordered q-particle creation and annihilation operators. The formulae have the same formal expressions as fermionic and bosonic ones but differ by a nature of fields. This allows us to derive the perturbation series for the theory and develop analogues of standard quantum field theory constructions in q-functional form.