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Then the dominant excitation in the hadronic phase is a massless pion, while that in the quark-gluon plasma is massless quarks and gluons. Here the infinite product is taken for all possible momentum states.įor simplicity we consider chiral limit (i.e., vanishing mass) and a vanishing chemical potential, which experiments ensure at high energy. In Case of BosonsĪt finite temperature and chemical potential, the grand canonical partition function for noninteracting massive bosons with internal degrees of freedom is given by where is the occupation number for each quantum state with energy with mass and is the momentum of the particle. Then, the thermodynamical equations such as pressure and energy density of quark-gluon plasma are obtained. In this section, we derive the thermodynamics of QGP in case of bosons and fermions taking into account the GUP impact. Thermodynamics of Quark-Gluon Plasma with GUP Effect The results, discussions, and conclusions are given in Sections 3 and 4. In Section 2, we derive thermodynamics of QGP consisting of a noninteracting massless bosons and fermions with impact of GUP approach. Then, these corrections with bag model are used to describe the quark-gluon plasma equation of state and compare it with QCD lattice results. We calculate the corrections to various thermodynamic quantities, like the energy density and the pressure. In this paper, the effect of the GUP on QGP equation of state of massless quark flavors at a vanishing chemical potential is studied. Recently, another approach based on super gravity was implemented to QCD and to QGP especially. These effects were investigated on condensed matter, atomic systems, the Liouville theorem (LT) in statistical mechanics, and the weak equivalence principle (WKP). Since the GUP modifies the Hamiltonian, it is important to study these effects quantitatively. Also, can be interpreted as the momentum at low energies and at high energies. Hence, the momentum would be subject of a modification and becomes where and satisfy the canonical commutation relations. The Generalized Uncertainty Principle (GUP) corresponding to it reads which yields a minimal observable length. In other minimal length formalism, the Heisenberg algebra associated with the momentum and the position coordinates is given by where is the minimal length parameter. The Generalized Uncertainty Principle was implemented on deriving the thermodynamics of ideal quark-gluon plasma of massless quark flavor. In particular, exact solutions of various relativistic and nonrelativistic problems have been obtained in the presence of a minimal length. Also, in quantum optics, the GUP implications can be measured directly which confirm the theoretical predictions. Thus, quantum mechanics can be studied in the presence of a minimal length. These approaches seem to modify almost all mechanical Hamiltonians. One of the most exciting predictions of some approaches related to quantum gravity, perturbative string theory, and black holes is the minimal length concept existence. IntroductionĮssential modifications in Heisenberg’s uncertainty principle are predicted near Planck scale which is called Generalized Uncertainty Principle (GUP). One can notice that the asymptotic behavior which is characterized by Stephan-Boltzmann limit would be satisfied.
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The exciting point is the large value of bag pressure especially in case of flavor which reflects the strong correlation between quarks in this bag which is already expected. The main features of QCD lattice results were quantitatively achieved in case of, , and flavors for the energy density, the pressure, and the interaction measure. We find a significant effect for the GUP term. The Generalized Uncertainty Principle is implemented on deriving the thermodynamics of ideal QGP at a vanishing chemical potential. The quark-gluon plasma (QGP) equation of state within a minimal length scenario or Generalized Uncertainty Principle (GUP) is studied.