Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: \(P(\phi)_2\)-model on a finite volume
type: Item
instance of: scholarly article
title: Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: \(P(\phi)_2\)-model on a finite volume
zbMATH Open document ID: 1179.81075
author: Shigeki Aida
published in: Journal of Functional Analysis
publication date: 2009-06-04T00:00:00Z
review text: [For Part I, see the author, ibid. 203, No.~2, 401--424 (2003; Zbl 1038.81027).] The semi-classical limit of the lowest eigenvalue of a \(P(\phi)_2\)-Hamiltonian on a finite volume interval is determined. The problem is formulated in setting of abstract Wiener space and the condition of existence of such a limit is established as the main result (theorem) of the paper. The key of the proof of this result is a large deviation estimate and Laplace's type asymptotic formula for Wick polynomials and a lower bound estimate of the Hamiltonian. It is suggested that the studies of the Schrödinger operators in large dimension and some works on renormalization may prove the main results of the paper.
reviewed by: Gheorghe Zet
Mathematics Subject Classification ID: 81Q20
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 5561675
zbMATH Keywords: semi-classical limit
zbMATH Keywords: \(P(\phi)\)-type Hamiltonian
zbMATH Keywords: quantum field theory
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.10.001
OpenAlex ID: W2058352044
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DOI: 10.1016/J.JFA.2008.10.001
description: scientific article; zbMATH DE number 5561675