约化相空间：规范理论的简化过程
Reduced phase space: quotienting procedure for gauge theories
摘要：
本文提出了一种基于位形-速度空间的前辛形式核的规范理论的约化方法。使用相空间程序获得的基础上，这个内核的本地表达式;在减少的相空间中的动态制定的障碍被识别和规避。我们表明，只要狄拉克猜想成立，这种减少过程是等价于标准狄拉克方法：狄拉克哈密顿量，包含主要的第一类约束，其拉格朗日乘子，可以扩大到一个扩展的狄拉克哈密顿量，其中包括所有的第一类约束没有任何变化的动态。即使它与标准狄拉克理论不同，但它总是等价于扩展狄拉克理论。当存在无效约束时，就会出现差异，在这些情况下，我们得出结论，标准狄拉克方法是更可取的-至少对于经典理论是这样。给出一个例子来说明这些功能，以及具有奇数物理自由度的相空间制剂的可能性。
英文摘要：
We present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase space procedures; the obstructions to the formulation of the dynamics in the reduced phase space are identified and circumvented. We show that this reduction procedure is equivalent to the standard Dirac method as long as the Dirac conjecture holds: that the Dirac Hamiltonian, containing the primary first class constraints, with their Lagrange multipliers, can be enlarged to an extended Dirac Hamiltonian which includes all first class constraints without any change of the dynamics. The quotienting procedure is always equivalent to the extended Dirac theory, even when it differs from the standard Dirac theory. The differences occur when there are ineffective constraints, and in these situations we conclude that the standard Dirac method is preferable --- at least for classical theories. An example is given to illustrate these features, as well as the possibility of having phase space formulations with an odd number of physical degrees of freedom.
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