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
We examine the consequences of the exchange statistics in one-dimensional systems with compact topology. As examples of nontrivial statistical behavior we calculate exactly the partition function and correlators for systems of free q particles on compactified chains. In particular, we consider a spin-1/2 XY chain with periodic boundary conditions that corresponds to the case of qϭ-1. For the case we report a representation of the two-point correlation functions at finite temperature. ͓S1063-651X͑96͒50708-7͔
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. *
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