IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
Worldline approach to quantum field theories on flat manifolds with boundaries
Autor/es:
F. BASTIANELLI, O. CORRADINI AND P.A.G. PISANI
Revista:
JHEP
Referencias:
Año: 2007 vol. 0702 p. 59 - 79
Resumen:
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.