标题： 简单参数化系统的量化 显示英文标题

标题： Quantization of simple parametrized systems

摘要： 我研究了一些简单参数化系统的规范形式和量子化，包括非相对论参数化粒子和相对论参数化粒子。 使用狄拉克的形式主义，我为每种情况构建了经典的约化相空间，并研究了对所使用的规范固定条件的依赖性。 这些系统的两个独立特性可能使这一构造变得困难：作用量在边界上不是不变的，而且约束可能具有不连通的解空间。 相对论粒子同时受到这两方面的影响，而非相对论粒子仅受第一方面的影响。 分析约化相空间中规范变换的作用，我表明规范固定的改变等价于一个规范变换。 在相对论情况下，对约束的一个分支在时间上进行量子化，并我分析了在哪些电磁背景中可以同时对两个分支进行量子化并仍然获得协变的幺正量子理论。 为了保持幺正性和时空协变性，除非没有电场，否则需要第二量子化。 我提出了所有这些情况下的内积定义，并推导出相对论情况下的克莱因-戈登内积。 我为BFV和法捷耶夫路径积分构建了幅度的相空间路径积分表示，从中推导出坐标空间中的路径积分（法捷耶夫-波波夫路径积分和几何路径积分）。 显示英文摘要

摘要： I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the classical reduced phase space and study the dependence on the gauge fixing used. Two separate features of these systems can make this construction difficult: the actions are not invariant at the boundaries, and the constraints may have disconnected solution spaces. The relativistic particle is affected by both, while the non-relativistic particle displays only by the first. Analyzing the role of canonical transformations in the reduced phase space, I show that a change of gauge fixing is equivalent to a canonical transformation. In the relativistic case, quantization of one branch of the constraint at the time is applied and I analyze the electromagenetic backgrounds in which it is possible to quantize simultaneously both branches and still obtain a covariant unitary quantum theory. To preserve unitarity and space-time covariance, second quantization is needed unless there is no electric field. I motivate a definition of the inner product in all these cases and derive the Klein-Gordon inner product for the relativistic case. I construct phase space path integral representations for amplitudes for the BFV and the Faddeev path integrals, from which the path integrals in coordinate space (Faddeev-Popov and geometric path integrals) are derived.