Tracking down gauge: an ode to the constrained Hamiltonian formalism
Tracking down gauge: an ode to the constrained Hamiltonian formalism
复制标题
追踪规范：对受约束的哈密顿形式主义的颂歌
DOI：
10.1017/cbo9780511535369.009
复制
发表时间：
2003
影响因子：
--
通讯作者：
J. Earman
中科院分区：
文献类型：
--
作者：
J. Earman
就像飞蛾被强光吸引一样，哲学家被浮华所吸引。因此，在讨论“规范”、“规范自由”和“规范理论”的概念时，他们往往把重点放在杨-米尔斯理论和纤维丛的数学装置上。但是，尽管杨-米尔斯理论对现代基本粒子物理学至关重要，但它们只是更广泛的规范理论中的一个特例。回顾过去，虽然纤维丛机制被证明是阐明杨-米尔斯理论结构的正确形式，但这种机制的长处也是它的弱点：纤维丛机制非常灵活和通用，因此，可以看到纤维丛潜伏在每一丛灌木之下、之上和周围。我们需要的是解释相关的束结构是什么，以及它是如何产生的，特别是对于那些最初不是用纤维束语言表述的理论。
在这里，我将描述一种方法，它产生于这样一种信念，即至少对于可以用拉格朗日/哈密顿形式表示的理论来说，规范自由恰好在存在适当性质的拉格朗日/哈密顿约束时出现。这一信念是共享的，如果只是心照不宣，由物理学界的一部分，工作在约束哈密顿系统。
Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language.
Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems.