INVESTIGADORES
GONZALEZ PISANI Pablo Andres
congresos y reuniones científicas
Título:
Teoría Cuántica de Campos en términos de Partículas Clásicas y Path Integrals en Variedades con Borde
Autor/es:
F. BASTIANELLI, O. CORRADINI AND P.A.G. PISANI
Lugar:
Buenos Aires
Reunión:
Encuentro; XIX Encuentro de la Strings@ar; 2006
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 + × 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 D using an image charge. The main technical difficulty lies in the fact that a smooth potential on + × D−1 extends to a potential which generically fails to be smooth on 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, A3 and A7/2. The calculation becomes sensibly harder as the perturbative order increases, and we are able to identify the complete A7/2
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.