Ziro Koba

Variation Principle in Relativistic Hydrodynamics

Recently Halatnikovll* has given a variation principle to derive the equations of the relativistic hydrodynamics. His procedure is based on the analogy to the relativistic particle dynamics. In this note it will be shown that an alternative variation method, which closely resembles that of field dynamics, can describe the behaviour of an ideal compressible fluid if one restricts oneself to the two limiting cases of extremely high and of extremely low temperatures. The law of energy-momentum conservation for the compressible fluid is expressed by2)

Hypothetical Velocity Measurements of a Dirac Particle

The characteristic behavior of a wave packet of a Dirac particle immediately after a precise position measurement, which is essentially due to the presence of inner degrees of freedom or the commutativity of the position and the velocity operators, is reinvestigated and compared with that of a fictitious one- component relativistic particle that is assumed to have only positive energy states. In order to distinguish this particle from a Dirac particle another hypothetical experiment of three successive position measurements is presented. Further, the procedure of this velocity measurement is analyzed by a three- dimensional treatment, which reveals the polarity of the Dirac electron and illustrates the non-commutativity of different components of the velocity. Finally the possibility of constructing sn arbitrarily small wave packet of a Dirac particle with positive energy states only, and the possibility of applying the present analysis to bosons are discussed.

Antinucleon Annihilation and Multiplicity of Emitted Pions

The large cross section and the high multiplicity of emitted pions are the most conspicuous features of nucleon-antinucleon annihilation experiments. A semiquantitative relation between these two facts is discussed. (A.C.)