AN ASYMPTOTIC ANALYSIS AND ITS APPLICATION TO THE NONRELATIVISTIC LIMIT OF THE PAULI-FIERZ AND A SPIN-BOSON MODEL

被引:30
作者
ARAI, A
机构
[1] Department of Mathematics, Hokkaido University
关键词
D O I
10.1063/1.528966
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
An abstract asymptotic theory of a family of self-adjoint operators {H κ}κ;>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the Pauli-Fierz model in quantum electrodynamics and of a spin-boson model. It is proven that the resolvent of Hκ converges strongly as K → ∞ and the limit is a pseudoresolvent, which defines an "effective operator" of Hκ at K ≈ ∞. As corollaries of this result, some limit theorems for Hκ are obtained, including a theorem on spectral concentration. An asymptotic estimate of the infimum of the spectrum (the ground state energy) of Hκ is also given. The application of the abstract theory to the above models yields some new rigorous results for them. © 1990 American Institute of Physics.
引用
收藏
页码:2653 / 2663
页数:11
相关论文
共 24 条
[1]  
[Anonymous], 1966, PERTURBATION THEORY
[2]   A NOTE ON SCATTERING-THEORY IN NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS [J].
ARAI, A .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1983, 16 (01) :49-69
[4]   SELF-ADJOINTNESS AND SPECTRUM OF HAMILTONIANS IN NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS [J].
ARAI, A .
JOURNAL OF MATHEMATICAL PHYSICS, 1981, 22 (03) :534-537
[5]  
ARAI A, 1989, HOKKAIDO U PREPRINT, V59
[6]  
BARUT A, 1980, F RAD THEORY QUANTUM
[7]   THE ELECTROMAGNETIC SHIFT OF ENERGY LEVELS [J].
BETHE, HA .
PHYSICAL REVIEW, 1947, 72 (04) :339-341
[9]  
Davies E. B., 1981, Annales de l'Institut Henri Poincare, Section A (Physique Theorique), V35, P149
[10]   ASYMPTOTIC ANALYSIS OF SOME ABSTRACT EVOLUTION EQUATIONS [J].
DAVIES, EB .
JOURNAL OF FUNCTIONAL ANALYSIS, 1977, 25 (01) :81-101