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arXiv 1302.5152hep-phhep-exnucl-th
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核子自旋有无穷多个分解吗?

Are there infinitely many decompositions of the nucleon spin ?

Masashi Wakamatsu

摘要:

讨论了胶子场分解为物理分量和纯规范分量的唯一性或非唯一性问题,这是最近提出的核子自旋的两种物理上不等价的规范不变分解的基础.认识到标准规范固定过程本质上是一个将无质量规范场的物理分量投影出来的过程,这一点是至关重要的。与阿贝尔情形相比,非阿贝尔规范理论的一个复杂之处在于,物理分量的封闭表达式只能用非定域威尔逊线给出,而威尔逊线通常是路径依赖的。我们知道,通过在空间和时间中选择一条无限长的直线路径,其方向由一个常数4矢量$n^μ$表征,我们可以覆盖一类称为一般轴向规范的规范,包括三种流行的规范,即时间轴向规范、光锥轴向规范和空间轴向规范。在这个一般的轴向规范下,我们计算了核子中夸克和胶子纵自旋的单圈演化矩阵。我们发现,最终的答案是完全相同的独立的选择$n^μ$,这相当于证明规范独立性和路径独立性的同时,虽然在一个有限的类的规范和路径。通过利用所有这些发现以及规范理论的成熟知识,我们反对在社会上迅速蔓延的观点,有无限多的核子自旋分解。

英文摘要:

We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. It is crucialy important to recognize the fact that the standard gauge fixing procedure is essentially a process of projecting out the physical components of the massless gauge field. A complexity of the nonabelian gauge theory as compared with the abelian case is that a closed expression for the physical component can be given only with use of the non-local Wilson line, which is generally path-dependent. It is known that, by choosing an infinitely long straight-line path in space and time, the direction of which is characterized by a constant 4-vector $n^μ$, one can cover a class of gauge called the general axial gauge, containing three popular gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within this general axial gauge, we have calculated the 1-loop evolution matrix for the quark and gluon longitudinal spins in the nucleon. We found that the final answer is exactly the same independently of the choices of $n^μ$, which amounts to proving the gauge-independence and path-independence simultaneously, although within a restricted class of gauges and paths. By drawing on all of these findings together with well-established knowledge from gauge theories, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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