Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: \(P(\phi)_2\)-model on a finite volume (Q1019704)

[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.