Abstract. The dynamics of quark-gluon plasma (QGP) as a lump of deconfined free quarks and gluons is elaborated. Based on the first principal, we construct the Lagrangian that represents the dynamics of QGP. To induce a hydrodynamics approach, we substitute the gluon fields with flow fields. As a result, the derived equation of motion (E.O.M) for gluon dominated QGP shows a form similar to Euler equation; and the energy momentum tensor also represents explicitly the system of ideal fluid. Combining the E.O.M and energy momentum tensor, the pressure and energy density distribution are analytically derived. IntroductionRecent experiments on heavy-ion collisions show a strong indication that hot dense deconfined phase of free quark and gluon, the so-called quark-gluon plasma (QGP), is conjectured to exist. The study of QGP itself has been carried out through a number of different approaches in previous works. Some results of these studies were obtained in the framework of quantum chromodynamics (QCD) theory by utilizing the lattice gauge calculation [1,2]. Other calculations of QGP were based on the relativistic hydrodynamics approach [3,4]. In the latter, the QGP could be either quark-[4] or gluon-[3] dominated matter. For the quark-dominated approach, a very small ratio of shear viscosity over entropy is required to get a good fit of the spectra of transverse momentum, energy density distribution and other physical observables that are obtained from experiments [5][6][7][8][9][10]. On the other hand, the gluon-dominated plasma motivated by the discoveries of jet quenching in the heavy-ion collision at Brookhaven's Relativistic Heavy Ion Collider (RHIC) indicates the shock waves in the form of Mach cone [11,12]. The present paper adopts the so-called fluid QCD model [13][14][15] to produce the equation of motion and energymomentum tensor for quark and gluon in a lump of QGP, and subsequently to investigate the distributions of the pressure and energy density. This paper is organized as follows. In Section 2 the fluid QCD model is briefly revisited, and the energy momentum tensor for ideal fluid is derived. Then, it is followed by the derivation for the equation of state and the explicit expression of gluon field in Section 3. Finally, the summary and discussion will be given in Section 4. Throughout this work, we use the natural units, i.e.,h = c = 1.
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