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591The theory of irreversible processes based on quantum statistical mechanics is formulated in th~ framework of the quautum field theory, for the purpose to investigate whether the hydrodynamical description is applicable to the meson cloud as considered in Landau's thoory 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 ao.d 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 co-· efficients to be 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. § 1. IntroductionFrom recent experiments of high energy cosmic rays, we could d~rive the following conclusions: (i) the sharp angular distribution of the energy flow of secondary particles in air showers, (ii) a small ratio of the number of heavy unstable particles ·and antinucleons to that of pions compared with that predicted by Fermi's theory 1 >, (iii) the multiplicity proportional to E0 1 / 4 -1 ' 3 , E 0 being the energy of an incident particle in laboratory system, and (iv) the value 0.2-0.7 of the inelasticity. The qualitative behaviors of the above characteristic features seem to be interpreted most successfully by Landau's. theory 2 l*** using a hydrodynamical model for the excited meson cloud formed in a Landau's model so far considered, one cannot calculate the inelasticity because of the implicit assumption that the entire initial energy is released from the colliding particles into their clouds. However,. there may be a possibility to calculate the inelasticity in the framework of Landau's theory with some modifications. at University of British Columbia on June 22, 2015 http://ptp.oxfordjournals.org/ Downloaded from We shall firstly define the hydrodynamical quantities from the field-theoretical at University of British Columbia on June 22, 2015 http://ptp.oxfordjournals.org/ Downloaded from * In what follows we shall denote the quantum operators by the Gothic type, while the arrows stand for the three dimensional vectors. ** Throughout this paper we use the unit :&"=c=l. at University of British Columbia on June 22, 2015 http://ptp.oxfordjournals.org/ ...

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