The aim of this review is to describe the field-theoretical foundations of Brout-Englert-Higgs (BEH) physics, and to show how the usual phenomenology arises from it. This requires to give a precise and gauge-invariant meaning to the underlying physics. This is complicated by the fact that concepts like the Higgs vacuum expectation value or the separation between confinement and the BEH effect loose their meaning beyond perturbation theory. This is addressed by carefully constructing the corresponding theory space and the quantum phase diagram. The physical spectrum needs then to be also given in terms of gauge-invariant, i. e. composite, states. Using gauge-invariant perturbation theory, as developed by Froehlich, Morchio, and Strocchi, it is possible to rederive conventional perturbation theory. This derivation explicitly shows why the description of the standard model in terms of the unphysical, gauge-dependent, elementary states of the Higgs and W-bosons and Z-boson, but also of the elementary fermions, is adequate and successful. These are unavoidable consequences of the field theory underlying the standard model, from which the usual picture emerges. The validity of this emergence can only be tested non-perturbatively. Such tests, in particular using lattice gauge theory, will be reviewed as well. They fully confirm the underlying mechanisms. It will be seen that the structure of the standard model is very special, and qualitative changes occur beyond it. The extension beyond the standard model will therefore also be reviewed. Particular attention will be given to structural differences arising for phenomenology. Again, non-perturbative tests of these results will be reviewed. Finally, to make this review self-contained a brief discussion of issues like the triviality and hierarchy problem, and how they fit into a fundamental field-theoretical formulation, is included.

中文翻译：

---

布劳特-恩格勒特-希格斯物理学：从基础到现象学

这篇综述的目的是描述布劳特-恩格勒特-希格斯 (BEH) 物理学的场论基础，并展示通常的现象学是如何从中产生的。这需要为基础物理赋予精确且规范不变的含义。由于诸如希格斯真空期望值或限制与 BEH 效应之间的分离等概念在扰动理论之外失去了其意义，这一事实使情况变得复杂。这是通过仔细构建相应的理论空间和量子相图来解决的。然后还需要根据规范不变（即复合）状态给出物理谱。使用由 Froehlich、Morchio 和 Strocchi 开发的规范不变扰动理论，可以重新推导传统的扰动理论。这个推导清楚地说明了为什么根据希格斯和 W 玻色子和 Z 玻色子的非物理、规范相关的基本状态以及基本费米子的非物理、规范相关的基本状态来描述标准模型是充分和成功的。这些是作为标准模型基础的场论不可避免的结果，通常的图景由此而出现。这种出现的有效性只能无扰动地进行测试。这些测试，特别是使用格子规范理论，也将被审查。他们完全证实了潜在的机制。可以看出，标准模型的结构非常特殊，超出它就会发生质的变化。因此，还将审查超出标准模型的扩展。将特别注意现象学引起的结构差异。再次，将对这些结果的非微扰测试进行审查。最后，为了使这篇评论自成一体，包括对琐碎性和层次问题等问题的简要讨论，以及它们如何适合基本的场论公式。