Quick Search:
Prog. Theor. Phys. Vol. 57 No. 5 (1977) pp. 1732-1748
General Ward-Like Relations in Canonical Field Theory
Yasushi Takahashi and
Tetsuo Gotō
Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada
(Received October 28, 1976)
Abstract:
Infinitesimal canonical transformation of a field operator is written in terms of the chronological product of the field operator and the generating current. This relation is then generalized to the infinitesimal transformation of the chronological (and retarded) products of any number of field operators. It is shown that the general relations thus obtained contain identities known as the generalized Ward relations in various forms.
The general relations given in integral form are converted into differential form. The relation to the similar identities obtained by the path integral method is discussed and use of the general relations is suggested.
The argument of a previous paper is, thus, refined and extended in three aspects: (i) constraint variables are treated systematically, (ii) it is pointed out that the general relations hold true for the retarded products, (iii) relation to the path integral method is discussed.
URL :
http://ptp.ipap.jp/link?PTP/57/1732/
DOI : 10.1143/PTP.57.1732
References:
- For example see, J. J. Sakurai, Currents and Mesons (University of Chicago Press, 1969.)
-
D. R. Yennie, S. C. Frautschi and H. Suura, Ann. of Phys. 13 (1961), 379[CrossRef].
-
E. S. Abers and B. W. Lee, Phys. Rep. C 9 (1973), 1[CrossRef].
M. Veltman, Proceedings of International Symposium on Electron and Photon Interaction at High Energies, (Bonn, 1974) p. 429.
-
H. Matsumoto, N. J. Papastamatiou and H. Umezawa, Nucl. Phys. B 68 (1974), 236[CrossRef];
ibid. 82 (1974), 45[CrossRef].
-
B. W. Lee, Phys. Rev. D 5 (1972), 823[APS].
G. T'Hooft, Nucl. Phys. B 33 (1971), 173[CrossRef].
A. Slavnov, Theor. Math. Phys. 10 (1972), 99.
-
J. Schwinger, Phys. Rev. 82 (1951), 914[APS].
- See, Y. Takahashi, An Introduction to Field Quantization (Pergamon, Oxford, 1968).
- R. Utiyama, Prog. Theor. Phys. 9 (1959), 19[PTP].
J. Schwinger, Phys. Rev. 125 (1962), 1043[APS];
ibid. 130 (1963), 402[APS].
- H. S. Green, Proc. Phys. Soc. A 66 (1953), 873.
- N. Nakanishi, Prog. Theor. Phys. 35 (1966), 1111[PTP].
N. Nakanishi, Prog. Theor. Phys. Suppl. No. 51 (1972), 1[PTP].
K. Yokoyama, Prog. Theor. Phys. 51 (1974), 1956[PTP].
- G. Källén, `Gradient Terms in Commutators of Currents and Fields', unpublished lecture note (1966).
M. Hayakawa and K. Yokoyama, Prog. Theor. Phys. 44 (1970), 533[PTP].
P. Gbase and A. Das, Prog. Theor. Phys. 46 (1971), 1623[PTP].
-
J. C. Taylor, Nucl. Phys. B 33 (1971), 436[CrossRef].
A. Salam and J. Strathdee, Nuovo Cim. A 11 (1972), 397.
B. de Wit and D. Z. Freeman, Phys. Rev. D 12 (1975), 2286[APS].
- Y. Takahashi, `The Divergence Identity and the Dynamical Rearrangement of Symmetry in the Conventional Field Theory', Preprint, May 1976.
-
L. Leplae, H. Umezawa and F. Mancini, Phys. Rep. C 10 (1974), 151[CrossRef].
See also, H. Matsumoto, H. Umezawa, `A Rigorous Formulation of the Boson Method in Supperconductivity', Preprint.
-
M. N. Shah, H. Umezawa and G. Vitiello, Phys. Rev. B 10 (1974), 4724[APS].
- K. Yokoyama and R. Kubo, Prog. Theor. Phys. 54 (1975), 848[PTP].
