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Lanczos-type potentials in non-Abelian gauge theories

1980; Springer Science+Business Media; Volume: 59; Issue: 1 Linguagem: Inglês

10.1007/bf02739050

2037-4895

W. K. Atkins, W. Rhett Davis,

Geophysics and Gravity Measurements

Here we investigate a variational approach for obtaining a potential structure for non-Abelian gauge theories by introducing identically satisfied constraints in a variational principle which is based on one that is identically satisfied. This technique for finding potentials for field theories was used by Lanczos (1962) to find his so-called thirdorder «spin» tensor in the context of Einstein's gravitational theory. In the case of general non-Abelian gauge theories, it is found that the Lanczos-type potentials are related to the usual potentials by generalized gauge transformations. This method is applied in the context ofSO 3 (orSU 2) gauge theory as well as Einstein and Einstein-Cartan gravitational theories. Various recent attempts to formulate gauge theories of gravity based on the Poincaré group are discussed. An application of the results of this paper shows that a mixed form of the Ricci coefficients of rotation can be used to display the gauge structure of the space-time curvature in essential agreement with the results of Hehlet al.