Tetsuo Gotō

ON THE SEPARATION OF REDUNDANT VARIABLES IN THE QUANTUM THEORY OF THE YANG-- MILLS FIELD.

Following close parallelism to the electrodynamics, the decomposition of the Yang-Mills Field is performed in the gauge invariant way. Thus, it is easily seen that gauge independent parts are transverse vector fields which are subjected to quantization. Elimination of redundant variables from the Hamiltonian is also performed by a unitary transformation. Essential difference from the arguments of Schwinger and Arnowitt-Fickler) is clarified throughout this note.

An Operator Formalism to the Path Integral Method

An operator formalism to the path integral method is developed. In this formalism the operator characterizing the trajectories of the particle is introduced and the usual path integral is expressed in terms of expectation value of a functional of that operator. We also investigate the Wiener-Hermite expansion on the basis of our operator formalism. Feynmans path integral is justified as a sort of analytic continuation of the path integral in the Wiener process.

On the nature of the electromagnetic field

In an attempt to identify the electromagnetic fields as an affine connection for spinors, the natures of the electromagnetic interaction and the electric charge are investigated. All spinors interact with the electromagnetic field. The possibility of charge independence is studied. The violation of the charge independence by the electromagnetic field is apparently caused by the violation of the flatness of space-time. (auth)