(Received June 8, 1953)
By generalizing the method formerly developed by the author, the energy-momentum tensor is obtained also for the case of non-localized interactions. It comes out that the interaction part of this tensor is not given simply by -L'δµν as due to Kristensen-Møller and Bloch, and that the total tensor satisfies the equation of continuity as a consequence of the equations of motion. As the result of the space integration of the µ4 component of the tensor, a general and simple expression of the energy-momentum 4-vector is derived in terms of δ functions and sign functions of the time. This vector turns out to be the constant of motion owing to the continuity equation. The same is true of the case of current density and total charge. Thus, it may be asserted contrary to the opinion of Kristensen-Møller and Bloch that it is always possible to construct not only the constants of collision but also the constants of motion when the invariant Lagrangian is given. The problem is now to consider the physical significance of the expressions and how to perform the quantization upon Heisenberg representation.
URL : http://ptp.ipap.jp/link?PTP/10/125/
DOI : 10.1143/PTP.10.125