Two-dimensional parallel transport : combinatorics and functoriality
| dc.creator | Attal, Romain | |
| dc.date | 2001-05-31 | |
| dc.date | 2001-10-17 | |
| dc.date.accessioned | 2026-07-07T04:28:29Z | |
| dc.date.available | 2026-07-07T04:28:29Z | |
| dc.description | We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These "sweeping functors" transport fiber bundles with connection along a surface whereas usual connections transport a group element along a path. We show that to get rid of the parametrization, we must use Abelian degrees of freedom. In the general, non-Abelian case, we conjecture that the smooth limit of this construction provides us with representations of the group of diffeomorphisms of the swept surface. Applications to gauge theories are proposed. | |
| dc.description | 18 pages ; v2 : interpretation of abelianisation changed and typos corrected | |
| dc.identifier | https://arxiv.org/abs/math-ph/0105050 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0105050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56807 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 18F20 ; 53C05 ; 53C29 ; 55U10 | |
| dc.title | Two-dimensional parallel transport : combinatorics and functoriality | |
| dc.type | text |