权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Nonperturbative analysis of charged-particle-system interacting with a quantum field

带电粒子系统与量子场相互作用的非微扰分析

基本信息

批准号：
15540191
负责人：
HIROSHIMA Fumio
金额：
$ 1.6万
依托单位：
Setsunan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

The spectrum of Hamiltonians describing a system of charged particles interacting with a quantum field is nonpertubatively studied. It can be regarded as the spectral analysis of a self-adjoint operator on a tensor product of infinite dimensional Hilbert spaces. Mainly an electron minimally coupled with photons, and the so-called Nelson model are investigated by means of functional analysis and functional integrals. The purpos of the present project is as follows : (1)estimates of the number of bosons in ground states, (2)to prove the tightness of Gibbs measures, (3)estimates of the multiplicity of ground states of a Hamiltonian without cutoffs, (4)the decay of the Green functions of a certain spin model. Our achievements are as follows.For (1)by virtute of an application of asymptotic fields of spectral scattering theory in the quantum field theory we got some results which are submitted as the paper entitledRegularities of ground states in quantum field models (with Arai and Hirokawa)For (2)it is obtained some results for a polaron type model of the Pauli-Fierz model by means of a functional integral representation of a heat semigrounp. The result will be submitted somewhere as soon as possible.For (3)an upper bound of the multiplicity of ground states of a Hamiltonian defined through a quadratic form, which is new as far as we know. It is submitted as the paper entitledMultiplicity of ground states in quantum field modelsWe find that this method can be applied for a generalized spin-boson model.A result concerning (4)is obtained for the so-called O(N)-spin model, and now we are writing a paper for this.Throughout this project we can investigate a mass renormalization of the nonrelativistic QED, and we got some results contrary to a conventional physical claim, which is submitted as the paper entitledMass renormalization in nonrelativistic QED with spin 1/2 (with K.R.Ito)

非微扰地研究了描述带电粒子与量子场相互作用系统的哈密顿量谱。它可以看作是无限维Hilbert空间张量积上的自伴算子的谱分析。主要用泛函分析和泛函积分的方法研究了电子与光子的最小耦合，以及所谓的Nelson模型。本项目的目的如下：(1)基态玻色子数目的估计，(2)证明Gibbs测度的紧密性，(3)无截止的哈密顿量基态多重性的估计，(4)某种自旋模型的格林函数的衰变。我们的成果如下：(1)借助于光谱散射理论的渐近场在量子场论中的应用，我们得到了一些结果，这些结果被提交为论文《量子场模型中基态的规律性(Arai和Hirokawa)》。(2)通过热半圆的泛函积分表示，得到了Pauli-Fierz模型的极化子类型模型的一些结果。结果将尽快提交到某个地方。对于(3)通过二次型定义的哈密顿量的基态多重数的上界，这是我们所知的新的。这篇论文的题目是《量子场模型中基态的多重性》。我们发现这个方法可以应用于广义的自旋-玻色子模型。对于所谓的O(N)-自旋模型，我们得到了关于(4)的一个结果，现在我们正在为此写一篇论文。通过这个项目，我们可以研究非相对论QED的质量重整化，我们得到了一些与传统物理主张相反的结果，这篇论文是以自旋为1/2的非相对论QED中的质量重整化(与K.R.Ito)相反的