(Received August 17, 1970)
It is shown that a symmetric tensor field of the second rank Aµν(x) should be introduced in order to retain the invariance of the action-integral under a generalized translation xµ→xµ+ξµ(x), provided that the original action-integral is invariant under inhomogeneous Lorentz transformations. It is further proved that the generalized gauge field Aµν should appear in the Lagrangian in exactly the same fashion as the metric tensor gµν does in Einstein's theory of gravitation.
Some general feature is also discussed with respect to a law of conservation of some physical quantity which becomes no longer valid when the interaction with the generalized gauge field takes place, provided that the associated group is non-Abelian.
URL : http://ptp.ipap.jp/link?PTP/45/612/
DOI : 10.1143/PTP.45.612