Prog. Theor. Phys. Vol. 55 No. 1 (1976) pp. 287-296
Inevitable Surface Dependence of Some Operator Products and Integrability
Department of Physics, Osaka University, Toyonaka, Osaka 560
*Department of Physics, University of Osaka Prefecture, Sakai, Osaka 591
**Institute of Physics, College of General Education, Osaka University, Toyonaka, Osaka 560
(Received June 13, 1975)
In general even in local theory the operator products at the same space-time point must be considered as a limit of non-local products. It is natural to confine non-locality on a space-like surface. In this case some operator products with three or more constituents possess an inevitable and purely quantum-mechanical surface dependence. Taking the pion-nucleon system as an example, we explicitly calculate in the order of g2 this kind of the surface dependence of the interaction Hamiltonian. In order to obtain a consistent theory, this surface is required to be identified with the space-like surface in the Tomonaga-Schwinger equation. Then the interaction Hamiltonian needs an additional, non-canonical and surface-dependent term, which can be derived uniquely from the canonical Hamiltonian. The integrability of the Tomonaga-Schwinger equation is proved by taking account of this surface dependence together with the gradient term in the equal-time commutator.
DOI : 10.1143/PTP.55.287
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Citing Article(s) :
Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 241-257
Boson Field Description of Fermions in Two Dimensions
Azuma Tanaka and Kunio Yamamoto