q-Functional Field Theory for particles with exotic statistics

TL;DR

This paper develops a quantum field theory framework for systems of interacting particles with exotic statistics, introducing q-functional derivatives, perturbation series, and diagram techniques, with applications to one-dimensional systems.

Contribution

It introduces a novel q-functional field theory approach for exotic particles, extending standard methods to new statistical regimes.

Findings

Derived formulae for partition functions and Green's functions using q-functional derivatives.

Established a perturbation series and diagram technique for q-particle systems.

Compared theoretical results with exact solutions in one-dimensional models.

Abstract

In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we derive formulae in q-functional derivatives for the partition function and Green's functions generating functional for systems of exotic particles. This leads to a corresponding perturbation series and a diagram technique. Results are illustrated by a consideration of an one-dimensional q-particle system and compared with some exact expressions obtained earlier.