Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-21
JHEP 0702:059,2007
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 6 figures. Minor rephrasing of a few sentences, references added. Version accepted by JHEP
Scientific paper
10.1088/1126-6708/2007/02/059
We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^{D-1} which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full R^D using an image charge. The main technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1} extends to a potential which generically fails to be smooth on R^D. This implies that standard perturbative methods fail and must be improved. We propose a method to deal with this situation. As a result we recover the known heat kernel coefficients on a flat manifold with geodesic boundary, and compute two additional ones, A_3 and A_{7/2}. The calculation becomes sensibly harder as the perturbative order increases, and we are able to identify the complete A_{7/2} with the help of a suitable toy model. Our findings show that the worldline approach is viable on manifolds with boundaries. Certainly, it would be desirable to improve our method of implementing the worldline approach to further simplify the perturbative calculations that arise in the presence of non-smooth potentials.
Bastianelli Fiorenzo
Corradini Olindo
Pisani Pablo A. G.
No associations
LandOfFree
Worldline approach to quantum field theories on flat manifolds with boundaries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Worldline approach to quantum field theories on flat manifolds with boundaries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Worldline approach to quantum field theories on flat manifolds with boundaries will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-22141