The difficulties of the classical theory of the electron are examined and methods to eliminate them are given. It is shown that the whole theory can be derived from a division of the total field created by a point charge in two parts, one which reacts on the generating particle and accounts for the emission of radiation, another which does not react on the praticle but acts on other particles. There are several types of motions of the particles depending on the kind of field they generate, fields which are always solutions of Maxwell's equations. Only three types of motions are, apparently, physically interesting: (a) motions with positive or negative kinetic energy in which the particles radiate, and (b) radiationless motions analogous to the stationary motions of quantum theory. It is shown that the field picture of Faraday and Maxwell must be revised because npt all the electric actions between particles can be considered as arising from their interaction with a field. The whole theory of the particles and the field can be derived from an action principle and boundary conditions for the equations of motion of the particles and the field. * This paper is a reduced and somewhat generalized form of a more extensive paper sent to
Methods similar to those of second quantization are applied to the Liouville équation of the classical statistical mechanics. An équa tion similar to the Schrodinger équation of a quantized field is given. It is shown that the interprétation rules of the quantal type of the field formalism lead to the rules of the classical statistical mechanics, the particles being treated as indistinguishable. The application of the Fock treatment of second quantization leads to the introduction of wave funct ions in phase space, the probability density of the classical statistical mechanics being the square of the absolute value of the wave function in phase space. The choice of the sign in the commutation rules of the field operators leads to symmetrical or antisymmetrical wave functions in phase space. To each kind of symmetry corresponds a différent statistics, Bose or Permi, as in quantum theory. The Boltzmann statistics cor responds to phase space wave functions without symmetry conditions. The wave functionals for the states with zéro particles of the fields in phase space are analogous to those of the quantized fields of quantum theory. 1. Introduction. The method of second quantization was first introduced by DIR AC in the quantum theory of Systems of non interacting Bose particles and later extended by JOR DAN and KLEIN (^) to the case of interacting Bose particles, and by
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