Quick Search:

uzh logo
Browse by:

Zurich Open Repository and Archive

Maintenance: Tuesday, July the 26th 2016, 07:00-10:00

ZORA's new graphical user interface will be relaunched (For further infos watch out slideshow ZORA: Neues Look & Feel). There will be short interrupts on ZORA Service between 07:00am and 10:00 am. Please be patient.

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22131

Cattaneo, A S; Cotta-Ramusino, P; Rinaldi, M (1999). Loop and path spaces and four-dimensional BF theories: connections, holonomies and observables. Communications in Mathematical Physics, 204(3):493-524.

Accepted Version
View at publisher


We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows.
For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B).
In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non-topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.


11 citations in Web of Science®
11 citations in Scopus®
Google Scholar™



38 downloads since deposited on 27 Jan 2010
9 downloads since 12 months

Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Deposited On:27 Jan 2010 12:09
Last Modified:05 Apr 2016 13:26
Publisher DOI:10.1007/s002200050655

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page