• Corpus ID: 119709288

# Functional Integration on Constrained Function Spaces I: Foundations

```@article{Lachapelle2012FunctionalIO,
title={Functional Integration on Constrained Function Spaces I: Foundations},
author={J. Lachapelle},
journal={arXiv: Mathematical Physics},
year={2012}
}```
• J. Lachapelle
• Published 3 December 2012
• Mathematics
• arXiv: Mathematical Physics
Analogy with Bayesian inference is used to formulate constraints within a scheme for functional integration proposed by Cartier and DeWitt-Morette. According to the analogy, functional counterparts of conditional and conjugate probability distributions are introduced for integrators. The analysis leads to some new functional integration tools and methods that can be applied to the study of constrained dynamical systems.
2 Citations
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield
The algebraic approach to quantum mechanics has been key to the development of the theory since its inception, and the approach has evolved into a mathematically rigorous \$C^\ast\$-algebraic

## References

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Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield
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We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several
This is a self-contained paper which introduces a fundamental problem in the calculus of variations, the problem of finding extreme values of functionals. The reader should have a solid background in