Wednesday, December 5, 2012

1212.0502 (J. LaChapelle)

Functional Integration on Constrained Function Spaces    [PDF]

J. LaChapelle
Analogy with Bayesian probability theory is used to study constrained physical systems within the context of functional integration. Since functional integrals probe function spaces, both kinematic and dynamic 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.
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