QUANTUM RELATIVISTIC HYDI~ODYNAMICS SYSTEMS WITH BROKEN SYMMETBY. I. LOCAL-EQUILIBRIU M STATE OF
Alexander V. Prozorkevich, V. L. Samorodov, S. A. Smolyanskiǐ
The nonequilibrium statistical operator method is used to construct a two-velocity relativistic hydrodynamics of a quantum-field system with broken symmetry and complex scalar order parameter. The approach is based on model expansions of the operators (the energy-momentum tensor, the current density, etc.) used for statistical description of the system in the hydrodynamic stage. In the first part of the paper, these expansions are used to construct the statistical operator and the thermodynamics of a local-equilibriu m state. Below, we construct a quantum relativistic two-velocity hydrodynamics on the basis of first principles using Zubarev's nonequilibrium statistical operator method (11}. In Sec.2, we establish the connection between the 4-velocity of the motion of the ordered component with the gradient of the phase of the order parameter. In Sec.3 we note that the methods of (2-7) based on the use of unitary transformations in the Galileo group to obtain the equations of two-velocity hydrodynamics do not admit direct generalization to the relativistic domain. In this connection, we propose an approach based on model expansions of the energy-momentum tensor and the current density (and, possibly, other operators used for statistical des- cription of systems in the hydrodynamic stage). These expansions are then used in Sec.4 to construct the statistical operator and the thermodynamics of the local-equilibrium state. The transport relations and the hydrodynamic equations will be discussed in Part If. Below, we use a system of units in which c = l~ = k = 1. The signature of the metric tensor is
•Jan 1, 1983•0 citations