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Journal of Physics A Mathematical and General

Many-body problems with composite particles and q-Heisenberg algebras

Sidney S. Avancini, Gastão I. Krein

Published Feb 7, 1995• 58 citations
Publisher

Abstract

We propose to employ deformed commutation relations to treat many-body problems of composite particles. The deformation parameter is interpreted as a measure of the effects of the statistics of the internal degrees of freedom of the composite particles. A simple application of the method is made for the case of a gas of composite bosons.
DOI
10.1088/0305-4470/28/3/021

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A formalism for treating the many-body problem of composite particles is presented for the case of composite particles consisting of two fermions. Commutation relations for composite-particle operators are derived, as well as a sum rule satisfied by the composite-particle Green's function. In an approximation that shuts off the interactions between composite particles in a consistent manner, the dynamical equation for the one-composite-particle Green's function is solved and the distribution function for the composite particles obtained. Possible applications to real systems are discussed.
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We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us to describe the interacting gas of composite (two-fermionic or two-bosonic) bosons. Using the relevant generalization of the Jackson derivative, we derive a two-parametric expression for the total number of particles, from which the deformed virial expansion of the equation of state is obtained. The latter is interpreted as the virial expansion for the effective description of a gas of interacting composite bosons with some interaction potential.
Abstract A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a generalized transformation. Using this generalization, we were able to construct a special representation called the “Composite Particle Representation”. In the composite, particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical representation which includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons from the quark point of view and the Interacting Boson Model in nuclei.
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We propose to consider nonlinear fluctuations in the theory of liquid 4 He deforming the commutation relations between the generalized coordinates and momenta.Generalized coordinates are coefficients of density fluctuations of Bose particles.The deformation parameter takes into account the effects of three-and four-particle correlations in the behavior of a system.This parameter is defined from the experimental values of the elementary excitation spectrum and the structure factor extrapolated to T = 0 K.The numerical estimation of the ground state energy and the Bose condensate fraction is made.The elementary excitation spectrum and the potential of interaction between the helium atoms are recovered.