作为完整约束的逆Higgs现象
Inverse Higgs phenomena as duals of holonomic constraints
摘要：
逆希格斯现象在具有戈德斯通玻色子（如晶体中的声子）的物理系统中起着重要作用，它涉及非完整力学约束。通过制定场论的对称性和约束，在一般的方式使用微分几何的语言，我们表明，许多例子中的约束逆希格斯现象属于一个特殊的类，我们称之为coholonomic约束，这是对偶（在范畴论的意义上）完整的约束。正如完整约束一样，具有共完整约束的系统等价于无约束系统（其自由度被称为本质戈德斯通玻色子），这使得研究它们的一致性和动力学变得更容易。在文献中的逆希格斯现象的其余例子需要对偶的一个轻微的概括的完整约束，我们称之为（co）meronomic。我们的形式主义简化和澄清了许多特设的假设和结构，目前在文献中。特别是，它确定了哪些是必要的，哪些只是方便。它也为研究更一般的动力学例子开辟了道路，包括没有明确定义的目标空间概念的系统。
英文摘要：
The inverse Higgs phenomenon, which plays an important rôle in physical systems with Goldstone bosons (such as the phonons in a crystal) involves nonholonomic mechanical constraints. By formulating field theories with symmetries and constraints in a general way using the language of differential geometry, we show that many examples of constraints in inverse Higgs phenomena fall into a special class, which we call coholonomic constraints, that are dual (in the sense of category theory) to holonomic constraints. Just as for holonomic constraints, systems with coholonomic constraints are equivalent to unconstrained systems (whose degrees of freedom are known as essential Goldstone bosons), making it easier to study their consistency and dynamics. The remaining examples of inverse Higgs phenomena in the literature require the dual of a slight generalisation of a holonomic constraint, which we call (co)meronomic. Our formalism simplifies and clarifies the many ad hoc assumptions and constructions present in the literature. In particular, it identifies which are necessary and which are merely convenient. It also opens the way to studying much more general dynamical examples, including systems which have no well-defined notion of a target space.
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