  We analyze the worldline formalism in the presence of a gravitational
background. In the worldline formalism a path integral is used to quantize the
worldline coordinates of the particles. Contrary to the simpler cases of scalar
and vector backgrounds, external gravity requires a precise definition of the
ultraviolet regularization of the path integral. Taking into account the UV
regularization, we describe the first quantized representation of the one-loop
effective action for a scalar particle. We compute explicitly the contribution
to the graviton tadpole and self-energy to test the validity of the method. The
results obtained by usual field theoretical Feynman diagrams are reproduced in
an efficient way. Finally, we comment on the technical problems related to the
factorization of the zero mode from the path integral on the circle.
