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Clustering in many-quark systems: the two-nucleon problem
Skip to main content. Log In Sign Up. The colourlessness partition function of the quantum quark-gluon gas. The effect of this constraint on the thermodynamical properties of the systems is considered.
The exciting prospect of discovering the observable signals of quark-gluon matter formation in heavy ion collisions has recently led to a comprehensive theoretical study of quark-gluon systems .
But the most reliable results of these investigations concentrate mainly on limiting behaviour.
In particular, the starting point for many papers is the important result that a sufficiently hot or dense matter displays a simple thermodynamical kte iour corresponding to an ideal quark-gluon gas. At decreasing temperature or density the strongly interacting matter should exhibit more and more hadronic behaviour. It makes it necessary to take consideration of both the quak order terms in the perturbative treatment of the quark-gluon gas and the nonperturbative effects .
We argue here that the correct inclusion of colour quark-gluon degrees of freedom is important, too. The hypothesis of colour confinement demands the realization of coloufless states singlets of the SU Nc group of a q u a r k – gluon system only.
As the complicated dynamical problem of confinement is not yet solved we must regard the colourless constraint of the allowed states of a quark-gluon system as a subsidiary requirement in describing the global thermodynamical equilibrium state .
The purpose of this note is to calculate the singlet partition func- tion of a quantum quark-gluon gas with the SU 3 colour group. Let us suppose that single-particle states transform under a certain representation a of the internal symmetry group G. In the general case G is a compact semi-simple n-parameter Lie group. Multiparticle states 1however, do not transform under the irreducible representation of the group G.
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Then the problem under consideration is to calculate the kttr function corresponding to the irreducible representation v, under which our quark-gluon system is transformed in what follows we are interested in a situ- ation where v is the singlet. Thus, the problem of calculating Z v in eq. The idea of the abovementioned construction is to avoid dealing with the complicated sys- tem of state vectors by using a rather simple basis 1 wuark compute eq.
We have for eq. At large V the spectrum of single-particle states becomes a quasicontinuous one and Formulae 5 and 8 give a formal solution of our problem.
To perform concrete calculations we need to have an explicit form of the invariant measure and the character of the fundamental quark representation of SU 3 group. We would like to note that the exponential power in eq. Substituting the explicit expressions of the characters we have for the exponential power in eq. The analysis shows that the dominant contribution to the integral of eq.
The additional preexponential factor in eq. The consideration of this correction is important at least in two points.
First it generates the corrections in the thermodynamical quantities for finite systems. Let us estimate values of the corrections 81 and 8 2 from the data of relativistic heavy ion collisions. It was shown in ref.
Secondly and it is more essential the power corrections in the partition function 11 are equivalent to the power corrections in the state density “mass spectrum” of quark-gluon bags r m, o m is a mass of bag and o is its volume. The colourlessness constraint changes dor values of the parameters 7 and 8 in eq.
But it was emphasized in ref. The character and even the possibility of a phase transition between the bag gas and the quark-gluon plasma is determined by these values.
References [ 1] W. Gelobenko, Compact Lie groups and their representations Nauka, Moscow, Marichev, Integrals and series Nauka, Moscow, Remember me on this computer.
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