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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.

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. 

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.

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.

I was asking OP.

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