|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
Path space forms and surface holonomy
A p-form on path space PM can be constructed from a p-form and a p+1-form on the space M. Similarly from a Lie algebra valued 1-form A and a Lie algebra valued 2-form B on Principal fiber bundle one can construct a connection on path space bundle. But a single group is not sufficient for non Abelian description of surface holonomy ("No go" theorem)! Introducing another group one can define a 'consistent' surface holonomy for the non Abelian case. This introduction of second group leads to an interesting categorical picture of the surface holonomy. As in pathspace a 'point'is basicaly a 'path' in base space, path space formalism can be very useful to study dynamics of an extended object like string.