The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field

被引：43

作者：

Lorinczi, J ^{[1
]}

Minlos, RA

Spohn, H

机构：

[1] Tech Univ Munich, Zentrum Math, D-80290 Munich, Germany

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Dobrushin Math Lab, Moscow 101447, Russia

来源：

ANNALES HENRI POINCARE | 2002年 / 3卷 / 02期

关键词：

Scalar Field; Field Model; Quantum Particle; Massless Scalar; Unitarily Equivalent;

D O I：

10.1007/s00023-002-8617-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not unitarily equivalent with the Hamiltonian obtained from Euclidean quantization. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Fock space and the two Hamiltonians are unitarily equivalent. We also show that the Euclidean Hamiltonian has no spectral gap.

引用

页码：269 / 295

页数：27

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