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

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

URL: http://arxiv.org/abs/2208.12446v1
Date: Fri, 26 Aug 2022 05:53:19 GMT
Title: The Berezin-Simon quantization for K\"ahler manifolds and their path integral representations
Authors: Hideyasu Yamashita
Abstract summary: 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.
Score: 0.2741266294612775
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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