Prog. Theor. Phys. Vol. 31 No. 2 (1964) pp. 311-321
On the Commutation Relation for the Canonical Energy Density
Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken
(Received September 19, 1963)
The interaction Hamiltonian in the interaction representation for an arbitrary spin field coupled to the external gravitational field is obtained by using the method which is the extension of Yang-Feldman's one. The equal time commutator for the canonical energy density is derived directly from the integrability condition of the Schrödinger equation in the interaction representation. It is shown that the presence of ordinary interactions among fields does not alter drastically the form of commutator for free fields and also the relation between the present method and Schwinger's one based on the extended conservation law is discussed.
DOI : 10.1143/PTP.31.311
J. Schwinger, Phys. Rev. 127 (1962), 324[APS].
See also, P. A. M. Dirac, Rev. Mod. Phys. 34 (1962), 592[APS].
J. Schwinger, Phys. Rev. 130 (1963), 406[APS];
ibid. 130 (1963), 800[APS].
K. Johnson, Nucl. Phys. 25 (1961), 431[CrossRef].
J. Schwinger, Phys. Rev. Lett. 3 (1959), 296[APS].
R. Utiyama, Phys. Rev. 101 (1956), 1597[APS].
For instance, O. Costa de Beauregard, Phys. Rev. 129 (1963), 466[APS].
- Y. Takahashi and H. Umezawa, Prog. Theor. Phys. 9 (1953), 14[PTP]; ibid. 9 (1953), 501[PTP].
Y. Katayama, Prog. Theor. Phys. 10 (1953), 31[PTP].
C. N. Yang and D. Feldman, Phys. Rev. 79 (1950), 972[APS].
- H. A. Buchdahl, Nuovo Cim. 25 (1962), 486.
H. Umezawa and A. Visconti, Nucl. Phys. 1 (1956), 348[Elsevier].
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- This formula can be also derived by the straightforward method as shown by
J. C. Garrison, Phys. Rev. 129 (1963), 1424[APS].
Citing Article(s) :
Progress of Theoretical Physics Vol. 33 No. 3 (1965) pp. 510-523
An Attempt to Derive the Gravitational Potential
Progress of Theoretical Physics Vol. 54 No. 3 (1975) pp. 914-916
A Comment on the First Event of Possible ΔS/ΔQ=-1 Process
Shuzo Ogawa, Yu-ichi Yamamoto and Tsutomu Yanagida