content_image/373436.jpg content_image/373437.jpg content_image/373438.jpg content_image/373439.jpg
ensemble in the following way 

<img src='content_image/373436.jpg'>

where a is real and positive and b and c are real. The invariance Haar measure for Sp ( N ) is approximated to 

<img src='content_image/373437.jpg'>

The result for the canonical partition function with the symplectic symmetry group can be extrapolated around the saddle points to take the following general formula 

<img src='content_image/373438.jpg'>

where Z ( θ$_{1}$, θ$_{2}$, · · · , θ$_{N}$ ) ≈ Z$_{0}$ ( { θ$_{i}$ ≈ 0 } ) e − 1 2 a ∑ i $_{=1}$θ 2 i . The abbreviation (I.S.) means that the internal structure and the group variables satisfy the constraint ( θ$_{1}$ − π ) ≤ θ$_{2}$ ≤ · · · ≤ θ$_{2}$$_{N}$ ≤ ( θ$_{1}$ + π ). When the unimodular-like constraint is imposed (i.e. ∑ N i θ$_{i}$ = 0), the color-singlet state of the (unimodular-like) symplectic canonical ensemble is reduced to 

<img src='content_image/373439.jpg'>

## IV. EQUATION OF STATE FOR COMPOSITE NUCLEAR MATTER 

The color-singlet-state unitary (mixed-grand) canonical ensemble can be extrapolated to another color-singlet-state ensemble with different symmetry groups. The most important issue in the extrapolation from one symmetry group to another one is that these symmetry groups have the same number N$_{c}$ of fundamental Fourier color charges (i.e. group eigen- variables). The difference among various symmetry groups comes from the difference in the numbers of the conserved adjoint Fourier charges with the same number of fundamental Fourier charges. The second difference comes from the different invariance Haar measure for every kind of symmetry group. The invariance Haar measure for each symmetry group is essential in order to project the color-singlet-state of the quark and gluon bag. Therefore, the effective Vandermonde potential is modified drastically when the internal symmetry is transferred from one symmetry group to another one. 

