Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: \(P(\phi)_2\)-model on a finite volume

DOI10.1016/j.jfa.2008.10.001zbMath1179.81075OpenAlexW2058352044MaRDI QIDQ1019704

Shigeki Aida

Publication date: 4 June 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2008.10.001

zbMATH Keywords

quantum field theorysemi-classical limit\(P(\phi)\)-type Hamiltonian

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (3)

Precise Laplace asymptotics for singular stochastic PDEs: the case of 2D gPAM ⋮ Tunneling for spatially cut-off \(P(\phi)_2\)-Hamiltonians ⋮ Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions

Cites Work

• Leading large order asymptotics for \((\phi ^ 4)_ 2\) perturbation theory
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• Trace formulas, a Golden-Thompson inequality and classical limit in boson Fock space
• Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold
• Hypercontra ctive semigroups and two dimensional self-coupled Bose fields
• Logarithmic Sobolev Inequalities
• Splitting in large dimension and infrared estimates. II. Moment inequalities
• The double-well splitting of the low energy levels for the Schrödinger operator of discrete φ4-models on tori
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