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Is it possible to generalize quantum gauge theories?

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I know that there are nonabelian gauge theories and their supersymmetric extensions. Mathematically, gauge theories basing on the fact that one can introduce a fiber bundle with a Connection. From this the curvature (field strength) can be computed.

But what is when one has a non-smooth fiber bundle over the base manifold (minkowski spacetime) or some Special Kind of the gauge-groups? Are there existing generalizations for non-smooth gauge Groups(in physics, stochastic noise is sometimes regarded as non-smooth but the average of this noise function is smooth)?

This post imported from StackExchange Physics at 2015-02-10 13:50 (UTC), posted by SE-user kryomaxim

asked Feb 8, 2015 in Theoretical Physics by kryomaxim (65 points) [ revision history ]
recategorized Feb 10, 2015 by dimension10

For such a generalization, one has to have a physical motivation like an observable non-smooth field strength or so, I guess. Generalization for the sake of generalization may be useful, but it is a mathematical game first of all, in my opinion. I am not aware of such generalization, but I am not a specialist in this field.

commented Feb 10, 2015 by Vladimir Kalitvianski (102 points) [ no revision ]

A comment on a possible confusion: The gauge fields are connections on the principal bundle of the corresponding structure group. Tangent bundles are the ones we encounter in general relativity.

commented Feb 11, 2015 by conformal_gk (3,625 points) [ no revision ]

Can you give an example of 'non-smooth fiber bundle' or 'some Special Kind of the gauge-groups?' Not sure what you have in mind.

commented Feb 23, 2015 by gn0m0n (80 points) [ no revision ]

No I cannot. I do not know and nor can I see how it would work. Also my comment had not to do with your question, it was a clarification only.

commented Feb 24, 2015 by conformal_gk (3,625 points) [ no revision ]

I was asking OP.

commented Feb 24, 2015 by gn0m0n (80 points) [ no revision ]

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