arXiv 0912.51532009-12hep-thhep-lathep-ph

Gribov视界和i粒子：关于一个玩具模型和物理算符的构造

Gribov horizon and i-particles: about a toy model and the construction of physical operators

L. Baulieu, D. Dudal, M. S. Guimaraes, M. Q. Huber, S. P. Sorella, N. Vandersickel, D. Zwanziger

备注：: 35 pages, 10 .pdf figures. v2: version accepted for publication in Physical Review D
发表信息：: Phys.Rev.D82:025021,2010
DOI：: 10.1103/PhysRevD.82.025021

摘要：

将泛函积分限制在Gribov区域$Ω$，导致欧氏杨-米尔斯理论在红外区域的行为的深刻修改。例如，Gribov类型的胶子传播子$\frac{k^2}{k^4+{\hat γ}^4}$可以被看作是一对非物理模式的传播，这里称为$i$粒子，具有复数质量$\pm i{\hat γ}^2$。从这个观点来看，胶子是非物理的，人们可以把它们看作是被限制的。我们介绍了一个简单的玩具模型，描述了一组合适的复合运营商可以构建出$i$ -粒子的关联函数只表现出真正的分支削减，与相关的正谱密度。因此，这些复合算子可以被称为物理的，并且是Gribov-Zwanziger理论中胶球的玩具类比。

英文摘要：

Restricting the functional integral to the Gribov region $Ω$ leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region. For example, a gluon propagator of the Gribov type, $\frac{k^2}{k^4+{\hat γ}^4}$, can be viewed as a propagating pair of unphysical modes, called here $i$-particles, with complex masses $\pm i{\hat γ}^2$. From this viewpoint, gluons are unphysical and one can see them as being confined. We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of $i$-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.

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