Reconstruction theorem for groupoids and principal fiber bundles |
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Authors: | E E Wood |
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Institution: | (1) Department of Physics, Monash University, 3168 Clayton, Victoria, Australia |
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Abstract: | The loop space formulation of 3+1 canonical quantum gravity premises that all physical information is contained within the
holonomy loop functionals. This assumption is the result of the reconstruction theorem for a principla fiber bundle on a base
loop space. The gauge connection for interacting gauge theories is more appropriately and readily reconstructed on a path
space as opposed to a loop space. We generalize the reconstruction theorem to a base path space. Employing a holonomy groupoid
map and a path connection, we trivially construct an abstract Lie groupoid from which a principal fiber bundle and gauge connection
can be derived as distinctive examples. The groupoid reconstruction theorem is valid on both connected and nonconnected base
manifolds, unlike the holonomy group reconstruction theorem, which can only be utilized for connected manifolds. |
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