Self-Adjointness Criterion for Operators in Fock Spaces

被引：11

作者：

Falconi, Marco ^{[1
,2
]}

机构：

[1] Univ Rennes 1, IRMAR, F-35042 Rennes, France

[2] Univ Rennes 1, Ctr Henri Lebesgue, F-35042 Rennes, France

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2015年 / 18卷 / 01期

关键词：

Essential self-adjointness; Fock spaces; Interacting quantum field theories; Nelson Hamiltonian; Pauli-Fierz Hamiltonian; NELSON MODEL; FIELD-THEORY; FIERZ; ATOMS;

D O I：

10.1007/s11040-015-9173-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.

引用

页数：18

共 27 条

[1] Asymptotic completeness for a renormalized nonrelativistic hamiltonian in quantum field theory: The nelson model
Ammari Z.
[J]. Mathematical Physics, Analysis and Geometry, 2000, 3 (3) : 217 - 285
[2] Wigner Measures Approach to the Classical Limit of the Nelson Model: Convergence of Dynamics and Ground State Energy
Ammari, Zied
Falconi, Marco
[J]. JOURNAL OF STATISTICAL PHYSICS, 2014, 157 (02) : 330 - 362
[3] A THEOREM ON ESSENTIAL SELF-ADJOINTNESS WITH APPLICATION TO HAMILTONIANS IN NONRELATIVISTIC QUANTUM-FIELD THEORY
ARAI, A
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1991, 32 (08) : 2082 - 2088
[4] Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field
Bach, V
Fröhlich, J
Sigal, IM
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 207 (02) : 249 - 290
[5] Quantum electrodynamics of confined nonrelativistic particles
Bach, V
Frohlich, J
Sigal, IM
[J]. ADVANCES IN MATHEMATICS, 1998, 137 (02) : 299 - 395
[6] Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules
Bach, V
Fröhlich, J
Sigal, IM
Soffer, A
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 207 (03) : 557 - 587
[7] THE MATHEMATICS OF 2ND QUANTIZATION
COOK, JM
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1951, 37 (07) : 417 - 420
[8] Asymptotic completeness in quantum in field theory.: Massive Pauli-Fierz Hamiltonians
Derezinski, J
Gérard, C
[J]. REVIEWS IN MATHEMATICAL PHYSICS, 1999, 11 (04) : 383 - 450
[9] Spectral theory of Pauli-Fierz operators
Derezinski, J
Jaksic, V
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 180 (02) : 243 - 327
[10] Derezinski J., 2013, CAMBRIDGE MONOGRAPHS, DOI [10.1017/CBO9780511894541, DOI 10.1017/CBO9780511894541]

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