arXiv 0804.31212008-04hep-th

经典非对易规范理论的类粒子解

Particle-like solutions to classical noncommutative gauge theory

A. Stern

备注：: 21 pages
发表信息：: Phys.Rev.D78:065006,2008
DOI：: 10.1103/PhysRevD.78.065006

摘要：

我们构造了非对易U（1）规范理论的经典场方程在以下三种情况下的微扰静态解：a）时空非对易，b）空-空非对易，c）a）和b）都是.这些解在空间无穷远处趋向于库仑解，并且对于径向坐标$r$的中间值是有效的。它们在以原点为中心的半径为$r$的球体中产生自电荷，对于情况a），自电荷随着$r$的减小而增大，对于情况b），自电荷随着$r$的减小而减小。对于情况a），这可能意味着精确解屏蔽了原点处的无限电荷，而对于情况b），电荷密度在原点处表现良好是合理的，就像Born-Infeld电动力学中发生的那样。对于a）和b）两种情况，当$r$趋向原点时，中间区域的自能比库仑解的自能增长得更快。于是，在非对易理论中，经典自能的发散似乎比在相应的对易理论中更严重。我们计算了这些解对氢原子光谱的最低阶效应，并利用它们对时空和时空非对易尺度提出了实验上的限制。我们发现情况a）和b）具有不同的实验特征。

英文摘要：

We construct perturbative static solutions to the classical field equations of noncommutative U(1) gauge theory for the three cases: a) space-time noncommutativity, b) space-space noncommutativity and c) both a) and b). The solutions tend to the Coulumb solution at spatial infinity and are valid for intermediate values of the radial coordinate $r$. They yield a self-charge in a sphere of radius $r$ centered about the origin which increases with decreasing $r$ for case a), and decreases with decreasing $r$ for case b). For case a) this may mean that the exact solution screens an infinite charge at the origin, while for case b) it is plausible that the charge density is well behaved at the origin, as happens in Born-Infeld electrodynamics. For both cases a) and b) the self-energy in the intermediate region grows faster as $r$ tends to the origin than that of the Coulumb solution. It then appears that the divergence of the classical self-energy is more severe in the noncommutative theory than it is in the corresponding commutative theory. We compute the lowest order effects of these solutions on the hydrogen atom spectrum and use them to put experimental bounds on the space-time and space-space noncommutative scales. We find that cases a) and b) have different experimental signatures.

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