On a covariant approach for the one-soliton sector

Abstract

This paper is dedicated to study, at least up to some extent, the consistency of the covariant approach proposed by Jevicki for quantizing the one-soliton sector. We analyse the α-dependence of the contributions to the soliton self-mass at the order ℏ2 of the loop expansion. Since α is an arbitrary parameter, it must disappear from physical results. We find that the sum of two-loop Feynman graphs containing only ordinary vertices is not α-independent, in contradiction with the result reported by Jevicki for this part of the amplitude. The relevant point is that the proof of Faddeev and Korepin, explaining cancellation of zero-mode divergences in their approach, does not imply cancellation of α-dependent terms in the scheme of quantization of Jevicki. It is only after adding the contribution coming from the tadpole graph, which in turns contains a vertex generated by the Jacobian, that one arrives at an amplitude fully independent of α. Thus, the presence of the Jacobian appears to be very important not only for the problem of conspiracy, but also for establishing α-independence at each order of the loop expansion. Our results verify, al least partially, that the covariant approach of Jevicki is a consistent quantum formalism.