A study of the nature of the field theories of the electron and positron and of the meson
The field theories of the electron and positron and also of the meson are developed by means of a close analogy with the photon. The analogy consists in the representation of the tracks of these particles by means of null-geodesics. The choice of notation is guided by the attempt to arrive at a theory in which the lengths (h/m 0 c) and (e 2 /m 0 c 2 ) occur naturally without reference to the structure of the particles, and in which the concept of quantization of electric charge is included. It is found that these objects can be attained by assuming that an additional degree of freedom is necessary for the description of the particles. If this is regarded as an additional dimension, it is found that an exact analogy can be made with the field theories familiar in the theory of relativity. An important feature is the union, in a single tensor, of energy, momentum and current density. A certain arbitrariness, not unlike that associated with the Poynting vector, is revealed, and it is shown that if this is removed by making a definite choice of the magnitude of the magnetic moment of the electron and positron, the spin angular momefttum is ^hereby fixed at the value 1/2h. In the development of the meson field the analogy shows* that the nuclear sources of the field act as if contributing a current density analogous to a magnetic current density in the electromagnetic case. The use of the additional degreb of freedom in the sinusoidal form indicates that the ratio of the constants g 1 and g 2 introduced into field theories as measures of the strengths of the sources is determined by the mass of the particle emitted in the neutron-proton transition.