Evaluating Feynman path integrals via the polynomial path family

Gabriel Bouch, Philip L. Bowers

We present a difficult and detailed calculation of propagators for quadratic potentials using a filtration of the space of variational paths around the classical path by the dense set of polynomial paths filtered by degree. This presents evidence for a cohesive explanation of path integrals as limits of finite-dimensional integrations using a sequence of filtration measures determined for specific dense families of paths by the requirement that the limit yield the free particle propagator.