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Prog. Theor. Phys. Vol. 55 No. 1 (1976) pp. 287-296
Inevitable Surface Dependence of Some Operator Products and Integrability
Kazuyasu Shigemoto,
Yukio Taguchi,*
Azuma Tanaka and
Kunio Yamamoto**
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)
Abstract:
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.
URL :
http://ptp.ipap.jp/link?PTP/55/287/
DOI : 10.1143/PTP.55.287
References:
- S. Kanesawa and S. Tomonaga, Prog. Theor. Phys. 3 (1948), 1[PTP]; ibid. 3 (1948), 101[PTP].
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For the regularization by the artificial fields, W. Pauli and F. Villars, Rev. Mod. Phys. 21 (1949), 434[APS].
- For the normal product method, W. Zimmermann, Lectures on Elementary Particles and Quantum Field Theory, vol. 2 (MIT Press, Cambridge, Mass., 1970), p. 397;
Ann. of Phys. 77 (1973), 536[CrossRef];
ibid. 77 (1973), 570[CrossRef].
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For the regularization by the continuous dimension, G. 't Hooft and M. Veltman, Nucl. Phys. B 44 (1972), 189[CrossRef].
- For the regularization based on the integrability condition, K. Yamamoto, Prog. Theor. Phys. 52 (1974), 304[PTP].
- K. Yamamoto, Prog. Theor. Phys. 46 (1971), 1002[PTP].
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 241-257
:
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Boson Field Description of Fermions in Two Dimensions
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Azuma Tanaka and Kunio Yamamoto
