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Prog. Theor. Phys. Vol. 22 No. 3 (1959) pp. 403-429

[ Full Text PDF : FREE ACCESS (1555K) ]

Applicability Conditions of the Hydrodynamical Model of Multiple Production of Particles from the Point of View of Quantum Field Theory

Chikashi Iso, Kenju Mori* and Mikio Namiki**

Research Institute for Fundamental Physics, Kyoto University, Kyoto
*Department of Physics, Tokyo University of Education, Tokyo
**Department of Applied Physics, Waseda University, Tokyo

(Received June 10, 1959)

Abstract:

In the framework of quantum field theory, it is attempted to investigate whether the hydrodynamical description is applicable to the meson cloud produced in extremely high energy collision of nucleons as considered in Landau's theory of the multiple production of particles. The applicability conditions of the hydrodynamical model consist of local equilibrium and conditions for the possibilities of defining the local system in the meson cloud, which are prepared by the methods based on quantum statistical mechanics of irreversible processes. These conditions are examined by comparison of the correlation lengths and the relaxation times of the meson fluid with a characteristic length and time, in which the thermodynamical parameters, the temperature for example, of the fluid decrease or increase by an appreciable amount on a macroscopic scale. From such examinations, it may be concluded that the hydrodynamical model holds almost everywhere except in the front part of the cloud after the whole cloud spreads over a region whose size is the order of the correlation length. It is, however, emphasized that the interactions in the initial cloud directly after collision and in the front part of the expanding cloud can never be described by any statistical law or hydrodynamics. The fact that the front particles are never in any thermal equilibrium suggests that they remember some features of initial high energy interactions in the very small cloud. In other words, it is inferred that the distributions (for example, K/π ratio and the momentum or angular distribution) of the front particles may inform us about the interactions at very small distances. On the other hand the influences of initial interactions on the remaining cloud are only taken into account through the initial boundary conditions for the hydrodynamical equation. In addition to the above discussions, it is pointed out that the assumption of the perfect fluid used by Landau is not so good; it turns out that one can expect an increment of the number of particles through the final interactions. Finally it is discussed whether these characteristics may be consistent with the recnet experiments.


URL : http://ptp.ipap.jp/link?PTP/22/403/
DOI : 10.1143/PTP.22.403

[ Full Text PDF : FREE ACCESS (1555K) ] Citation:

References:

  1. M. Namiki and C. Iso, Prog. Theor. Phys. 18 (1957), 591[PTP].
    This will be quoted as I in the present paper. The related papers are cited there.
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