A Feynman-Kac Formula for Unbounded Semigroups

1999/07/27 by Barry Simon, Simon, Barry
Mathematics · Physics and Astronomy · #47D08 (Primary) 60J65 (Secondary) #81S40 #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #msc:47D08 #msc:60J65 #msc:81S40

paper · pdf · doi:10.48550/arxiv.math-ph/9907022

5 pages, LaTeX. To appear in Proc. Intl. Conf. on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Leipzig 1999

arxiv created 1999/07/27 · openalex publication_date 1999/07/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x) that obey (for all ε> 0): V(x) ≥ - ε|x|² - C_ε. Even though e^-tH is an unbounded operator, any ϕ, ψ∈ L² with compact support lie in D(e^-tH) and is given by a Feynman-Kac formula.

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