q-Functional field theory for particles with exotic statistics

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 onedimensional q-particle system and compared with some exact expressions obtained earlier. *

Para-Grassmann Variables and Coherent States

“…Moreover, the name "para-Grassmann" was used also for different other definitions, see for example [1], where some different variables, in connection with para-statistics, were defined. Finally let us mention that in [9,10], q-deformed classical variables and different techniques were introduced. We will use here the conventions of [3] for the definitions of a differential and integral calculus appropriate for these variables.…”

“…The study of different generalisations of Grassmann variables and their applications has attracted a great deal of interest in the last decades (see for example [1,2,3,4,5,6,7,8,9,10,11,12,13,14] and references therein).…”

Existence Results of a Nonlocal Fractional Symmetric Hahn Integrodifference Boundary Value Problem

“…Quantum calculus has been proposed in the last three decades. The q-calculus, one type of quantum presented by Jackson [1,2], has been extensively used in the studies of mechanics, calculus of variations, and other problems in physics [3][4][5][6][7][8][9][10][11][12][13]). In 1949, Hahn [14] presented the development of quantum calculus based on two parameters q and ω, which is called Hahn calculus.…”

On fractional $(p,q)$-calculus

“…There are recent works related to q-calculus as seen in [6][7][8]. The knowledge of q-calculus and difference equations can be applied to physical problems such as molecular problems [9], elementary particle physics, and chemical physics [10][11][12][13]. Then, the q-field theory was presented in 1995 [14].…”