(Received December 8, 1949)
As the generalization of the ordinary one-time theory, the super-many-time theory has been constructed, which enables us to calculate many problems with less ambiguities than the ordinary one, because of its covariant feature, but the results coincide with the ordinary ones.
Here, in this paper, we get a new result that the one-time theory can never deduce.
The most characteristic difference between two theories is the existence of the integrability condition, which occurs from the increasement of the number of wave equations. In fact, the number of wave equations in the super-many-time theory is continuous infinity, so that the condition for the existence of the solution of the wave equations is very severe. Concretely speaking, the condition that the wave equations have the uniquely determined solution, i. e. the integrability condition restricts the properties of the interaction Hamiltonian densities between fields.
First we discuss the possible structure of the Hamiltonian density by the leading principle, “the principle of action through a medium”. Next using the results, we prove that the energy-momentum conservation law requires the integrability condition in its proof. This signifies that the integrability condition is necessary not only for mathematical reason, but also for physical. Lastly as a concrete application of this condition, we deduce rule for the choice of various types of decays, which is the one that the one-time theory can never conclude.
URL : http://ptp.ipap.jp/link?PTP/5/187/
DOI : 10.1143/PTP.5.187