Multiple Production of Particles and Hydrodynamical Aspect of Quantum Theory of Fields

Abstract

The theory of irreversible processes based on quantum statistical mechanics is formulated in the framework of the quantum field theory, for the purpose to investigate whether the hydrodynamical description is applicable to the meson cloud as considered in Landau's theory of the multiple production of particles. The hydrodynamical quantities are defined from the field-theoretical operators by means of the averaging procedures in quantum statistical mechanics. Through the discussions about the relation between the equation of state of meson-nucleon fluid and the feature of interactions, it seems possible to conclude that at extremely high energy the equation of state assumed by Landau holds in the case of the first kind of interactions (having the dimensionless coupling constants), while it is not the case in the systems with the second kind of interactions (having the coupling constants with dimension). In particular, the violation of Landau's equation would be serious in the case of interactions with derivatives. Next the formulae are presented to calculate the phenomenological coefficients to the considered as the representatives of the properties of the fluid. Such a formulation includes the calculations of the relaxation time, the time for a system to reach the local equilibrium. There the methods are also prepared to estimate deviations from the macroscopic values of physical quantities predicted by the hydrodynamics due to fluctuations.