The Berezin-Simon quantization for Kähler manifolds and their path integral representations

2022/08/26 by Yamashita, Hideyasu
#51M15 #53D50 #60H10 #81R30 #81S40 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2208.12446

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) Kähler manifold which satisfies some conditions, with a Hamiltonian H:M→ℝ. For technical reasons, we consider only the cases where H is smooth and bounded. We use Güneysu's extended version of the Feynman--Kac theorem to formulate the path-integral formula.

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