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arXiv · 2406.14547

A Mathematical Definition of Path Integrals on Symplectic Manifolds

Joshua Lackman
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Abstract

We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We show that K\"{a}hler manifolds provide many computable examples and we emphasize those whose Bergman kernel is constant along the diagonal.

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Joshua Lackman. 2024-06-20. A Mathematical Definition of Path Integrals on Symplectic Manifolds. https://arxiv.org/abs/2406.14547

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