Functional Integration on Constrained Function Spaces
J. LaChapelle · arXiv (Cornell University) · 2012
Analogy with Bayesian inference is used to study constrained physical systems within the context of functional integration. Since functional integrals probe function spaces, both kinematical and dynamical constraints are treated simultaneously and on equal footing. Following the analogy, functional counterparts of conditional and conjugate probability distributions are introduced for integrators and then applied to some well-known examples of constrained functional integrals. The analysis leads to some new functional integration tools and methods. These are utilized to construct a model of the prime counting function as a constrained gamma process.