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arXiv · 2208.12446

The Berezin-Simon quantization for K\"ahler manifolds and their path integral representations

Hideyasu Yamashita
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Abstract

The Berezin--Simon (BS) quantization is a rigorous version of the ``operator formalism'' of quantization procedure. The goal of the paper is to present a rigorous real-time (not imaginary-time) path-integral formalism corresponding to the BS operator formalism of quantization; Here we consider the classical systems whose phase space $M$ is a (possibly non-compact) K\"ahler manifold which satisfies some conditions, with a Hamiltonian $H:M\rightarrow\mathbb{R}$. For technical reasons, we consider only the cases where $H$ is smooth and bounded. We use G\"uneysu's extended version of the Feynman--Kac theorem to formulate the path-integral formula.

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Hideyasu Yamashita. 2022-08-26. The Berezin-Simon quantization for K\"ahler manifolds and their path integral representations. https://arxiv.org/abs/2208.12446

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