标题： 环面相空间的量化 显示英文标题

标题： Quantization of a torus phase space

摘要： $R^2$和$S^1 \times S^1$相空间的量化通过调整几何量子化的技术被明确进行。 关键在于左不变和右不变向量场的综合使用。 规范基、算子及其作用被明确给出。 应用了狄拉克以及吴岳和杨振宁关于单极子的论点，以获得相空间面积的量子化。 在无限维前量子希尔伯特空间中状态的等价性导致了一个物理希尔伯特空间，其维度等于普朗克常数单位下的相空间面积。 这些技术可以应用于任何具有辛结构的流形。 显示英文摘要

摘要： Quantization of $R^2$ and $S^1 \times S^1$ phase spaces are explicitly carried out tweaking the techniques of geometric quantization. Crucial is a combined use of left and right invariant vector fields. Canonical bases, operators and their actions are explicitly presented. Arguments of Dirac and also Wu and Yang for monopoles are applied for obtaining the quantization of the phase space area. Equivalence of states in the infinite dimensional prequantum Hilbert space resulting in a physical Hilbert space of dimension equal to the phase space area in units of the Planck constant is demonstrated. These techniques can be applied to any manifold with a symplectic structure.