Based on the first principle calculation, a Lagrangian for the system describing quarks, gluons, and their interactions, is constructed. Ascribed to the existence of dissipative behavior as a consequence of strong interaction within quark-gluon plasm
a (QGP) matter, auxiliary terms describing viscosities are constituted into the Lagrangian. Through a kind of phase transition, gluon field is redefined as a scalar field with four-vector velocity inherently attached. Then, the Lagrangian is elaborated further to produce the energy-momentum tensor of dissipative fluid-like system and the equation of motion (EOM). By imposing the law of energy and momentum conservation, the values of shear and bulk viscosities are analytically calculated. Our result shows that, at the energy level close to hadronization, the bulk viscosity is bigger than shear viscosity. By making use of the conjectured values $eta / s sim 1 / 4pi$ and $zeta / s sim 1$, the ratio of bulk to shear viscosity is found to be $zeta / eta > 4 pi$.
A Lagrangian density for viscous quark-gluon plasma has been constructed within the fluid-like QCD framework. Gauge symmetry is preserved for all terms inside the Lagrangian, except for the viscous term. The transition mechanism from point particle f
ield to fluid field, and vice versa, is discussed. The energy momentum tensor that is relevant for the gluonic plasma having the nature of fluid bulk of gluon sea is derived within the model. By imposing conservation law in the energy momentum tensor, shear viscosity appears as extractable from the equation.
