Relativistic commutation rules in the quantum theory of fields (II)

Abstract

Summary The analysis of the commutation rules between field variables at different times, begun in the first part of this paper 1) , is extended to more general cases, in connection with the Heisenberg-Pauli quantum theory of wave fields 2) . This theory is discussed in connection with the wave equations of the classical field. The theory involves difficulties in the case of first order equations of motion. It is shown that the commutation rules between field quantities at different times can be determined by means of the commutation rules at the same time and the equations of motion, when these equations are linear. The case of second order wave equations is explicitely treated, the commutation rules for the same time being known from the Heisenberg-Pauli theory. The study of the functions involved in the relativistic rules shows that the knowledge of these functions is equivalent to the complete solution of the wave equations, any solution being calculable by integrations involving the initial values.