Prog. Theor. Phys. Vol. 39 No. 3 (1968) pp. 830-846
Limiting Process of Cutoff and Auxiliary Fields in Quantum Field Theory. I
Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken
(Received October 12, 1967)
A tentative approach to a simplified model, by which the model is reformulated in order to derive no infinity before renormalization, is investigated. To achieve the view a limiting process of an invariant cutoff and a pair of auxiliary fields with indefinite metrics are introduced. These auxiliary fields are set up in such a way that they play the role of canceling out all divergences due to the original interaction of the model but not destroying the unitarity of the S-matrix within a Hilbert space with the positive metric. These circumstances are ensured by the limiting process of the cutoff. Self-masses of particles become finite. Nevertheless, their values are not determined on account of the presence of arbitrary parameters. It is to be thought that the different values of these parameters distinguish mass corrections to individual particles due to some unknown internal interactions for which one has no means of description. In a phenomenological viewpoint the presence of such parameters is rather convenient. Extension of the approach to other realistic theories seems to be possible.
DOI : 10.1143/PTP.39.830
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Citing Article(s) :
Progress of Theoretical Physics Vol. 40 No. 5 (1968) pp. 1143-1150
Convergent Field Theory with Non-Linear Non-Local Interaction
Progress of Theoretical Physics Vol. 43 No. 2 (1970) pp. 531-551
Quantum Electrodynamics with Infinitesimal Nonlinear Interactions
Progress of Theoretical Physics Supplement No.51 (1972) pp. 1-95
Indefinite-Metric Quantum Field Theory