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Prog. Theor. Phys. Vol. 38 No. 2 (1967) pp. 491-507

[ Full Text PDF : FREE ACCESS (894K) ]

Extended Translation Invariance and Associated Gauge Fields

Kenji Hayashi and Tadao Nakano*

Department of Physics, Kyoto University, Kyoto
*Department of Physics, Osaka City University, Osaka

(Received April 1, 1967)

Abstract:

Gauge fields together with non-linear field equations to govern them are introduced by requiring that the Lagrangian should be invariant under an extended translation in space-time, i.e. a translation in which four parameters are replaced by four arbitrary coordinate-dependent functions. A prescription is given to convert a non-invariant canonical (“pseudo”) energy-momentum tensor into an invariant one.
The symmetric part of these field equations is examined for the two cases: (1) under linear and non-relativistic approximation, it reduces to the classical gravitational-field equation, (2) for static and spherically symmetric field, its solution is shown to correspond to Schwarzschild's solution. The antisymmetric part has no classical analogues, for there are no sources of skew-symmetric energy-momentum tensors in the classical experiments. A reasonable method is proposed to eliminate this redundant field.


URL : http://ptp.ipap.jp/link?PTP/38/491/
DOI : 10.1143/PTP.38.491

[ Full Text PDF : FREE ACCESS (894K) ] Citation:

References:

  1. For example, C. N. Yang and R. L. Mills, Phys. Rev. 96 (1954), 191[APS].
  2. See, for example, Kōdi Husimi, Lecture on Variational Principle in Field Theory in 1943 at the Meeting of Japan Physical Society (edited by the Japan Ministry of Education, 1944).
    Earlier references are listed in detail therein.
  3. R. Utiyama, Phys. Rev. 101 (1956), 1597[APS].
  4. T. W. B. Kibble, J. Math. Phys. 2 (1961), 212[CrossRef].
    D. W. Sciama, Festschrift for Infeld (Pergamon Press, New York, 1961), p. 415. We are indebted to Dr. Kei Semba for informing us of this paper.

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