Gauge bosons at zero and finite temperature
Gauge bosons at zero and finite temperature
复制标题
DOI：
10.1016/j.physrep.2012.11.002
复制
发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
A. Maas
中科院分区：
文献类型：
--
作者：
A. Maas
Yang-Mills类型的规范理论是粒子物理标准模型的最重要的组成部分。它们是强相互作用和弱相互作用的组成部分，在它们的阿贝尔版本的电磁学中。由于杨-米尔斯理论是规范理论，它们的基本粒子，规范玻色子，不固定规范就无法描述。因此，为了获得它们的性质，量子化和量规固定的设置是必要的。在微扰理论之外，非阿贝尔规范理论中的规范固定受到Gribov-Singer模糊性的阻碍，这需要引入非局部约束。构建和实现一种方法无关的规范固定处方来解决这种模糊性是超越微扰理论描述规范玻色子的最重要的第一步。本文描述了推广摄动朗道规范的这一程序的建议。以晶格规范理论和量子运动方程两种方法为例，讨论了它们的实现。在测量固定之后，可以详细地研究测量玻色子。它们的关联函数提供了最直接的访问。在所有能量尺度上给出了相应的两点和三点相关函数。这使得我们可以获得规范玻色子的特性，比如它们不存在于渐近物理状态空间中，高能量下的类粒子特性，以及运行耦合。此外，还引入了仪表固定过程中的辅助自由度，并对其性质进行了讨论。这些结果提出了二，三，和四维，并为各种规范代数。最后，给出了有限温度下规范玻色子性质的修正。这些都反映了杨-米尔斯理论的相结构。然而，发现相变不能定义规范玻色子，尽管体热力学行为是斯特凡-玻尔兹曼型的。文中还提出了解决这一明显矛盾的方法。此外，这项决议为林德问题提供了明确和建设性的解决办法。因此，这里提出的技术和概念框架可以作为确定杨-米尔斯理论中相关函数的基础，从而开辟了研究直接实践相关性理论的途径。我们将简要地描述这一努力的现状，以及它与微扰理论以外的杨-米尔斯理论的其他研究方法的联系。
Gauge theories of the Yang–Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang–Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary. Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov–Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion. After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two- and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras. Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang–Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan–Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem. Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang–Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang–Mills theory beyond perturbation theory.