  The computation of anomalies in quantum field theory may be carried out by
evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation
of these Jacobians can be cast in the form of a quantum mechanical problem,
whose solution has a path integral representation. For the case of Weyl
anomalies, also called trace anomalies, one is immediately led to study the
path integral for a particle moving in curved spaces. We analyze the latter in
a manifestly covariant way and by making use of ghost fields. The introduction
of the ghost fields allows us to represent the path integral measure in a form
suitable for performing the perturbative expansion. We employ our method to
compute the Hamiltonian associated with the evolution kernel given by the path
integral with fixed boundary conditions, and use this result to evaluate the
trace needed in field theoretic computation of Weyl anomalies in two
dimensions.
