(Received July 20, 1962)
It is shown that the baryon number conservation has a close relation to the asymptotic behavior of some matrix elements for a large space-like separation of their arguments. This circumstance arises from the fact that, when the baryon number is conserved, the support of the weight function in the Jost-Lehmann-Dyson representation for the commutator is somewhat narrower than in the most general case. The explicit proof is given by means of the perturbation theory.
When the support in the Jost-Lehmann-Dyson representation is narrowed in this way, one can prove the dispersion relations for the nucleon vertex function.
It is difficult to give the proof in every of the perturbation theory, because in general diagrams there may appear singularities which should be separated, and it has not been known how those singularities can be separated. It can be shown however, in a simple example, that the existence of those singularities only complicates the problem without worsening the situation. Thus there is a good reason to believe that the results obtained here is true, though not proved in every order.
URL : http://ptp.ipap.jp/link?PTP/28/1080/
DOI : 10.1143/PTP.28.1080