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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. First it generates the corrections in the thermodynamical quantities for finite systems. The character and even the possibility of a phase transition between the bag gas and the quark-gluon plasma is determined by these values.

The hypothesis of colour confinement quadk 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 [3].

References [ 1] W.

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The effect of this constraint on the thermodynamical properties of the systems is considered. But the most reliable results of these investigations concentrate mainly on limiting behaviour. At large V the spectrum of single-particle states becomes a quasicontinuous one and 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 additional preexponential factor in eq. Skip to main content.

Gelobenko, Compact Lie groups and their representations Nauka, Moscow, The consideration of this correction is important at least in two points. In particular, the starting point for many papers is the important result that a sufficiently hot or dense matter displays a simple thermodynamical behav- iour corresponding to an ideal quark-gluon gas. 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.

At decreasing temperature or density the strongly interacting matter should exhibit more and more hadronic behaviour. We have for eq.

We argue here that the correct inclusion of colour quark-gluon degrees of freedom is important, too. But it was emphasized in ref.

Substituting the explicit expressions of the characters we have for the exponential power in eq. The exciting prospect of discovering the observable signals of quark-gluon matter forr in heavy ion collisions has recently led to a comprehensive theoretical ror of quark-gluon systems [1].

Enter the email address you signed up with and we’ll email you a reset link. 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 to compute eq.

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We would like to note that the exponential power in eq. It makes it necessary to take consideration of both the higher order terms in the perturbative treatment of the quark-gluon gas and the nonperturbative effects [2]. The colourlessness partition function of the quantum quark-gluon gas. Marichev, Integrals and series Nauka, Moscow, It was shown in ref. Thus, the problem of calculating Z v in eq.

### Clustering in many-quark systems: the two-nucleon problem – IOPscience

Let us estimate values of the corrections 81 and 8 2 from the data of relativistic heavy ion collisions. Help Center Find new research papers in: Formulae 5 and 8 give a formal solution of our problem. Then the problem under consideration is to calculate the partition function corresponding to the irreducible representation v, under which our quark-gluon gor is transformed in what follows we are interested in a situ- ation where v is the singlet.

Multiparticle states 1however, do not transform under the irreducible representation of the group G. Log In Sign Up. In the general case G is ror compact semi-simple n-parameter Lie group.

Click here to sign up. The colourlessness constraint changes the values of the parameters 7 and 8 in eq. Let us suppose that single-particle states transform under a certain representation a of the internal symmetry group G. The analysis shows that the dominant contribution to the integral of eq.