（玻色子）质量满足（外禀）曲率
(Bosonic)Mass Meets (Extrinsic)Curvature
摘要：
本文从杨-米尔斯-希格斯规范理论的真空对基态的观点讨论了自发对称性破缺的机制。我们把真空看作是一个适当的丛中的一个部分，它自然地与最小的（一般的）希格斯势相关联。如果真空的不变性群是规范群的真子群，那么这样的真空自发地破坏了基本的规范对称性。我们表明，每一个真空的选择承认几何解释玻色子质量矩阵为“正常”部分。这些部分的频谱在流形上是恒定的，并且与所选择的真空无关。由于质量矩阵与所选真空的不变性群可交换，因此可以分解玻色质量矩阵的本征丛中对应于玻色的厄米矢量丛。这种分解是"粒子多重体“的物理概念的几何模拟。在这个意义上，"自由粒子“的基本概念在规范理论的几何背景下也是有意义的，只要规范对称性被真空自发破缺。我们还讨论了希格斯基布尔机制（“希格斯晚餐”）从几何的角度来看。原来，通常在讨论希格斯晚餐时遇到的“幺正规范”是纯粹的几何起源。特别地，我们讨论了旋转对称的Higgs势，并给出了幺正规范存在的一个充分必要条件。作为一个具体的例子，我们讨论了在这方面的粒子物理学的标准模型的电弱部门的一些细节。
英文摘要：
In this paper we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs potential. Such a vacuum spontaneously breaks the underlying gauge symmetry if the invariance group of the vacuum is a proper subgroup of the gauge group. We show that each choice of a vacuum admits to geometrically interpret the bosonic mass matrices as ``normal'' sections. The spectrum of these sections turns out to be constant over the manifold and independent of the chosen vacuum. Since the mass matrices commute with the invariance group of the chosen vacuum one may decompose the Hermitian vector bundles which correspond to the bosons in the eigenbundles of the bosonic mass matrices. This decomposition is the geometrical analogue of the physical notion of a ``particle multplet''. In this sense the basic notion of a ``free particle'' also makes sense within the geometrical context of a gauge theory, provided the gauge symmetry is spontaneously broken by some vacuum. We also discuss the Higgs-Kibble mechanism (``Higgs Dinner'') from a geometrical point of view. It turns out that the ``unitary gauge'', usually encountered in the context of discussing the Higgs Dinner, is of purely geometrical origin. In particular, we discuss rotationally symmetric Higgs potentials and give a necessary and sufficient condition for the unitary gauge to exist. As a specific example we discuss in some detail the electroweak sector of the standard model of particle physics in this context.
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