Schematic model for QCD at finite temperature

Abstract

Abstract:The simplest version of a class of toy models for QCD is presented. It is a Lipkin-type model, for the quark-antiquark sector, and, for the gluon sector, gluon pairs with spin zero are treated as elementary bosons. The model restricts to mesons with spin zero and to few baryonic states. The corresponding energy spectrum is discussed. We show that ground state correlations are essential to describe physical properties of the spectrum at low energies. Phase transitions are described in an effective manner, by using coherent states. The appearance of a Goldstone boson for large values of the interaction strength is discussed, as related to a collective state. The formalism is extended to consider finite temperatures. The partition function is calculated, in an approximate way, showing the convenience of the use of coherent states. The energy density, heat capacity *

Schematic model for QCD. I. Low energy meson states

“…[12] the fermion sector is described by a Lipkin type model [1], consisting of two levels, one at energy −ω f and the other at energy +ω f (see Fig. 1).…”

“…In Ref. [12] the most simple version of such a model was presented. Like the models mentioned at the beginning, it is based on a Lipkin type model and it consists of two levels for the description of quarks and antiquarks.…”

“…In Ref. [12] it is shown that the model is able to describe the appearance of a quantum phase transition at zero temperature, when the interaction is turned on, and a phase transition to the non interacting case at nonvanishing temperature. In Ref.…”

“…The discussion will concentrate on the behavior of the model at low energy, corresponding to the zero temperature regime of QCD. The study of the high energy behavior and the transition to the Quark Gluon Plasma [13,14] will be presented in the forthcoming paper of the series [15]. In section 2 the basic ingredients of the model are introduced, with the proposition of a Hamilton operator.…”

“…In Ref. [12] the basic features of the model were discussed. Only flavor singlet and spin zero mesons were taken into account.…”