Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space: I. Unbounded one particle Hamiltonians
From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), 16 p.
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author = {Aida, Shigeki},
title = {Semi-classical limit of the lowest eigenvalue of a {Schr\"odinger} operator on a {Wiener} space: {I.} {Unbounded} one particle {Hamiltonians}},
booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
series = {Ast\'erisque},
publisher = {Soci\'et\'e math\'ematique de France},
number = {327},
year = {2009},
zbl = {1194.81092},
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url = {http://www.numdam.org/item/AST_2009__327__1_0/}
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Aida, Shigeki. Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space: I. Unbounded one particle Hamiltonians, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), 16 p. http://www.numdam.org/item/AST_2009__327__1_0/

[1] S. Aida - "Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space", J. Funct. Anal. 203 (2003), p. 401-424. | Article | MR 2003354 | Zbl 1038.81027

[2] S. Aida, "Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold", J. Funct. Anal. 251 (2007), p. 59-121. | Article | MR 2353701 | Zbl 1127.58014

[3] S. Aida, "Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II. $P{\left(\varphi \right)}_{2}$-model on a finite volume", J. Funct. Anal. 256 (2009), p. 3342-3367. | Article | MR 2504528 | Zbl 1179.81075

[4] S. Albeverio & A. Daletskii - "Algebras of pseudodifferential operators in ${L}_{2}$ given by smooth measures on Hilbert spaces", Math. Nachr. 192 (1998), p. 5-22. | Article | MR 1626379 | Zbl 0910.47043

[5] A. Arai - "Trace formulas, a Golden-Thompson inequality and classical limit in boson Fock space", J. Funct. Anal. 136 (1996), p. 510-547. | Article | MR 1380661 | Zbl 0894.47059

[6] M. Dimassi & J. Sjöstrand - Spectral asymptotics in the semi-classical limit, London Mathematical Society Lecture Note Series, vol. 268, Cambridge Univ. Press, 1999. | MR 1735654 | Zbl 0926.35002

[7] L. Gross - "Logarithmic Sobolev inequalities", Amer. J. Math. 97 (1975), p. 1061-1083. | Article | MR 420249 | Zbl 0318.46049

[8] B. Helffer - Semiclassical analysis, Witten Laplacians, and statistical mechanics, Series in Partial Differential Equations and Applications, vol. 1, World Scientific Publishing Co. Inc., 2002. | Article | MR 1936110 | Zbl 1046.82001

[9] B. Helffer & F. Nier - Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians, Lecture Notes in Math., vol. 1862, Springer, 2005. | MR 2130405 | Zbl 1072.35006

[10] R. Léandre - "Stochastic Wess-Zumino-Witten model over a symplectic manifold", J. Geom. Phys. 21 (1997), p. 307-336. | Article | MR 1436309 | Zbl 0879.53027

[11] R. Léandre, "Cover of the Brownian bridge and stochastic symplectic action", Rev. Math. Phys. 12 (2000), p. 91-137. | Article | MR 1750777 | Zbl 0968.58027

[12] B. Simon - The $P{\left(\varphi \right)}_{2}$ Euclidean (quantum) field theory, Princeton Univ. Press, 1974, Princeton Series in Physics. | MR 489552 | Zbl 1175.81146

[13] B. Simon, "Semiclassical analysis of low lying eigenvalues. I. Nondegenerate minima: asymptotic expansions", Ann. Inst. H. Poincaré Sect. A (N.S.) 38 (1983), p. 295-308. | EuDML 76200 | Numdam | MR 708966 | Zbl 0526.35027

[14] B. Simon & R. Høegh-Krohn - "Hypercontractive semigroups and two dimensional self-coupled Bose fields", J. Functional Analysis 9 (1972), p. 121-180. | Article | MR 293451 | Zbl 0241.47029