论文标题
相位空间家族的定量
Quantisation of a Family of Phase Spaces
论文作者
论文摘要
我们解释说，当用不同的符号结构量化相位空间时，参数空间上的量子希尔伯特空间束具有自然的单一连接。然后，我们专注于符号矢量空间及其费米子对应物。在回顾了量子希尔伯特空间如何取决于物理参数，例如哈密顿量和非物理参数，例如极化的选择，我们研究了当相空间结构本身变化时，希尔伯特空间束的连接，曲率和相位。我们将结果应用于超级载体矢量空间上的两球符号结构及其费米子类似物的家族，并以可能的概括结论。
We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic counterparts. After reviewing how the quantum Hilbert space depends on physical parameters such as the Hamiltonian and unphysical parameters such as choices of polarisations, we study the connection, curvature and phases of the Hilbert space bundle when the phase space structure itself varies. We apply the results to the two-sphere family of symplectic structures on a hyper-Kähler vector space and to their fermionic analogue, and conclude with possible generalisations.
