A unified geometric framework for boundary charges and dressings: Non-Abelian theory and matter
A unified geometric framework for boundary charges and dressings: Non-Abelian theory and matter
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边界电荷和敷料的统一几何框架：非阿贝尔理论和物质
DOI：
10.1016/j.nuclphysb.2019.02.020
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发表时间：
2018
影响因子：
2.8
通讯作者：
A. Riello
中科院分区：
文献类型：
--
作者：
H. Gomes;Florian Hopfmüller;A. Riello
规范理论的边界是一个微妙的问题。任意边界选择通过诺特第二定理进入电荷计算，阻碍了将明确的物理电荷分配给局部规范对称性。用新的自由度取代任意的边界选择是不言而喻的。但是，具体来说，这种边界自由度是虚假的——即它们不是理论原始领域内容的一部分，并且必须在粘合后消失。我们应该如何将它们融入我们对场论的了解中？我们通过在杨-米尔斯理论的场空间中引入连接 1 形式 ϖ，以统一的几何方式解决这些问题。使用这种几何工具，辛几何的修改版本（这里称为“水平”）是可能的。与边界条件无关，这种形式主义赋予每个区域一个电荷的物理概念：水平诺特电荷。水平规范电荷总是消失，而对于以全局对称为特征的可约构型，全局电荷仍然会出现。字段内容本身被用作区分“规格”和“物理”的参考系；不需要新的自由度，例如群值边缘模式。不同的参考场选择会产生不同的ϖ，它们是希格斯酉规范和库仑规范等规范固定装置的近亲。但形式主义远远超出了规范固定的范围，例如通过避免格里波夫问题。对于 ϖ 的一种选择，由物质自由度凝聚产生的戈德斯通模式恰好扮演了已知群值边缘模式的角色，但在这里它们作为场空间中的首选坐标而不是新场出现。对于另一种选择，在阿贝尔情况下，ϖ恢复电子的狄拉克修饰。
Boundaries in gauge theories are a delicate issue. Arbitrary boundary choices enter the calculation of charges via Noether's second theorem, obstructing the assignment of unambiguous physical charges to local gauge symmetries. Replacing the arbitrary boundary choice with new degrees of freedom suggests itself. But, concretely, such boundary degrees of freedom are spurious—i.e. they are not part of the original field content of the theory—and have to disappear upon gluing. How should we fit them into what we know about field-theory? We resolve these issues in a unified and geometric manner, by introducing a connection 1-form,ϖ, in the field-space of Yang–Mills theory. Using this geometric tool, a modified version of symplectic geometry—here called ‘horizontal’—is possible. Independently of boundary conditions, this formalism bestows to each region a physical notion of charge: the horizontal Noether charge. The horizontal gauge charges always vanish, while global charges still arise for reducible configurations characterized by global symmetries. The field-content itself is used as a reference frame to distinguish ‘gauge’ and ‘physical’; no new degrees of freedom, such as group-valued edge modes, are required. Different choices of reference fields give differentϖ's, which are cousins of gauge-fixings like the Higgs-unitary and Coulomb gauges. But the formalism extends well beyond gauge-fixings, for instance by avoiding the Gribov problem. For one choice ofϖ, would-be Goldstone modes arising from the condensation of matter degrees of freedom play precisely the role of the known group-valued edge modes, but here they arise as preferred coordinates in field space, rather than new fields. For another choice, in the Abelian case,ϖrecovers the Dirac dressing of the electron.