The Wigner semi-circle law in quantum electro dynamics
The Wigner semi-circle law in quantum electro dynamics
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DOI：
10.1007/bf02099625
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发表时间：
1996-10
影响因子：
2.4
通讯作者：
L. Accardi;Y. Lu
中科院分区：
文献类型：
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作者：
L. Accardi;Y. Lu
本文将量子理论随机极限的基本思想应用于量子电动力学。这自然引发了对希尔伯特模上新型量子随机微积分的研究。我们的主要结果是，在由自由粒子（电子、原子等）通过最小耦合与量子电磁场相互作用组成的系统的弱耦合极限中，出现了一种新型的量子噪声，它存在于希尔伯特模块而不是希尔伯特空间中。此外，我们证明了极限场算子的真空分布不是通常的高斯分布，而是维格纳半圆定律的非线性变形。当前理论产生的第三个新对象是所谓的相互作用福克空间。一种福克空间，其中粒子空间中的量子不是独立的，而是相互作用的。所有这些新特征的起源是我们没有引入偶极子近似，但我们保留了指数响应项，将电子耦合到量子电磁场。这会在极限主场（量子噪声）的所有模式之间产生非线性相互作用，我们发现其显式表达可以被视为费米黄金法则的非线性推广。
In the present paper, the basic ideas of thestochastic limit of quantum theoryare applied to quantum electro-dynamics. This naturally leads to the study of a new type of quantum stochastic calculus on aHilbert module. Our main result is that in the weak coupling limit of a system composed of a free particle (electron, atom,...) interacting, via the minimal coupling, with the quantum electromagnetic field, a new type of quantum noise arises, living on a Hilbert module rather than a Hilbert space. Moreover we prove that the vacuum distribution of the limiting field operator is not Gaussian, as usual, but a nonlinear deformation of the Wigner semi-circle law. A third new object arising from the present theory, is the so-calledinteracting Fock space. A kind of Fock space in which thenquanta, in then-particle space, are not independent, but interact. The origin of all these new features is that we do not introduce the dipole approximation, but we keep the exponential response term, coupling the electron to the quantum electromagnetic field. This produces a nonlinear interaction among all the modes of the limit master field (quantum noise) whose explicit expression, that we find, can be considered as a nonlinear generalization of theFermi golden rule.