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Volumn 59, Issue 1, 1980, Pages 116-132

Lanczos-type potentials in non-Abelian gauge theories

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EID: 51249182284 PISSN: 03693554 EISSN: 18269877 Source Type: Journal
DOI: 10.1007/BF02739050 Document Type: Article

Times cited : (6)

References (27)

1
- 0000817169
- Gauge theories
- (1973) Physics Reports , vol.9 , pp. 1
- Abers, E.S.¹ Lee, B.W.²

8
- 84934650057
- In addition, we will follow the notations of J. Schouten: Ricci Calculus (Berlin, 1954).

11
- 84934650044
- These results show that the Lagrange multiplier H|bv^a, which maintains the generalized Bianchi identities as constraints against an arbitrary tensor F|bvμ^a can be identified (in terms of a special solution in a particular gauge frame) as the potential A|bv^a By analogy with constraints in mechanics we may think of the potential H|bv^a as manifesting itself as related to a «force of constraint» arising through an infinitesimal violation of the generalized Bianchi identities (C. Lanczos: The Variational Principles of Mechanics Toronto, 1949). It is also to be noted that the special solution H|bv^a= A|bv^a is not inconsistent with the apparent gauge invariance of the variational principle. In particular, a somewhat lengthy calculation shows that, if the solution corresponding to H|bv^a= A|bv^a is substituted back into the Lagrangian (3.1) and the following transformations are made: (for xε space-time). {fx121-1}. {fx121-2} then the resulting transformed Lagrangian differs from the untransformed Lagrangian by only a pure partial divergence, i.e. {fx121-3}

12
- 36149046360
- (1978) Rep. Prog. Phys. , vol.41 , pp. 1357
- Goddard, P.¹ Olive, D.²

14
- 36149046360
- (1978) Rep. Prog. Phys. , vol.41 , pp. 1357
- Goddard, P.¹ Olive, D.²

19
- 84934650048
- Equation (6.7.) is obtained from (6.5) subject to the gauge conditions (6.6 a)–(6.6 c) by use of the Ricci identities and the first contracted Bianchi identities.

20
- 84934650050
- C. W. Misner, K. S. Thorne and J. A. Wheeler: Gravitation (San Francisco, Cal., 1973), p. 391.

22
- 9344227202
- (1961) J. Math. Phys. (N. Y.) , vol.2 , pp. 212
- Kibble, T.W.B.¹

23
- 84934650036
- D. W. Sciama: in Recent Developments in General Relativity (New York, N. Y., and Warsaw, 1962).

27
- 0001469477
- Extended Translation Invariance and Associated Gauge Fields
- (1967) Progress of Theoretical Physics , vol.38 , pp. 491
- Hayashi, K.¹ Nakano, T.²

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