content_image/368943.jpg content_image/368944.jpg content_image/368945.jpg content_image/368946.jpg
canonical ensemble with the color-singlet SU ( N$_{c}$ ) state in order to be extrapolated to other symmetries. The internal orthogonal, unitary and symplectic symmetry groups with the unimodular constraint are reviewed in Sec. III. The equation of state for the nuclear matter that is dominated by the Hagedorn states is given in Sec. IV. The continuous Hagedorn mass spectra are derived for the unimodular-like unitary, orthogonal and symplectic ensembles. The role of the chiral phase transition is considered in Sec. V. Several scenarios for the deconfinement phase transition are presented in Sec. VI. Finally, the conclusion is presented in Sec. VII. 

## II. THE NUCLEAR MATTER FOR THE RELATIVISTIC HEAVY ION COLLI- SIONS 

The grand canonical partition function in the equilibrium reads 

<img src='content_image/368943.jpg'>

The thermodynamic quantities are determined from the grand canonical partition function as follows 

<img src='content_image/368944.jpg'>

for the grand potential density, charge density, entropy and energy density, respectively. The canonical partition function can be determined by the functional integration method. The Lagrangian construction is essential. The QCD Lagrangian for quarks and gluons is given by [55] 

where the covariance derivative and field strength, respectively, read 

<img src='content_image/368945.jpg'>

<img src='content_image/368946.jpg'>

