# 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} }

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

### Functional Integration on Constrained Function Spaces II: Applications

- Mathematics
- 2014

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…

### Functional Integral Approach to $C^*$-algebraic Quantum Mechanics

- Physics
- 2015

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…

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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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