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• W2004245160 abstract "By examining the implications of the usual physical assumptions for gauge theories we are led to a number of interesting structures which can be formulated in terms of moving frames. The first problem we consider is Faddeev's fiber bundle procedure for removal of gauge degeneracies from quantum fields. We show how the theory of moving frames can be related to the theory of fiber bundles. In the fiber bundle extra displacements and extra components of the gauge fields are included. These precisely remove the gauge degeneracies. In order to formulate this problem in the language of fiber bundles, we begin with a section detailing the algebra of forms in four dimensions and their associated operations (exterior differentiation, Hodge duality and the natural Hilbert product of forms). We then show how to form the action for the SO(3) fiber bundle. This opens the general question (implicitly answered by this example) of how to quantize in a fiber bundle. Next we examine the question of choice of local symmetry structure. First we consider a space whose local rotations do not form a group. By generalizing the structure equations for manifolds, we can study such a space. Second, in general relativity it is assumed that at any point one can choose an orthonormal basis and a vanishing connection. This corresponds to giving the zeroth, first, and second coefficient of a Taylor's expansion of the coordinate system. But manifolds flatter than those of general relativity do exist for which the structure is carried in the higher coefficients. We show how to give an action principle for them. Third, algebras more general than Lie algebras are possible local symmetries, e.g., superalgebras, the octonian algebra, and others violating the Jacobi relation. An action is given for a one-parameter family of quasi-Lie algebras which reduces to that of u(1) + su(2) in the zero limit of the parameter. Fourth, simple examples of actions for gauged superalgebras are given which do not include the full complexity of general relativity. Fifth, an easy derivation of the supergravity action is made; then generalized to a supergravity Weinberg-Salam-type model." @default.
• W2004245160 created "2016-06-24" @default.
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• W2004245160 date "1978-11-15" @default.
• W2004245160 modified "2023-09-25" @default.
• W2004245160 title "Fermions and bosons in a unified framework. III. Mathematical structures and physical questions" @default.
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• W2004245160 doi "https://doi.org/10.1103/physrevd.18.3777" @default.
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