薛定谔实现中的伪经典系统量子化
Quantization of Pseudoclassical Systems in the Schrödinger Realization
摘要：
在薛定谔图像中，我们研究了具有经典反对易变量的伪经典动力学系统的量子化。在偶数维空间中，我们用广义Gupta-Bleetman方法和约化相空间方法对这些可以看作粒子自旋经典模型的系统进行了数值计算。只要做最小的修改，薛定谔量子力学的标准结构就可以用于伪经典系统。我们推广了标准薛定谔范数，并实现了观测量和约束的正确伴随性。我们构造了对应于旋量的状态空间作为反对易变量的物理波函数，发现在物理子空间和鬼子空间中都存在超选择扇区。虽然狄拉克-凯勒理论中的内积与我们的理论不等价，但其物理态与狄拉克-凯勒费米子公式中的物理态同构。
英文摘要：
We examine the quantization of pseudoclassical dynamical systems, models that have classically anticommuting variables, in the Schrödinger picture. We quantize these systems, which can be viewed as classical models of particle spin, using the generalized Gupta-Bleuler method as well as the reduced phase space method in even dimensions. With minimal modifications, the standard constructions of Schrödinger quantum mechanics of constrained systems work for pseudoclassical systems. We generalize the standard Schrödinger norm and implement the correct adjointness properties of observables and constraints. We construct the state space corresponding to spinors as physical wave functions of anticommuting variables, finding that there are superselection sectors in both the physical and ghost subspaces. The physical states are isomorphic to those of the Dirac-Kähler formulation of fermions though the inner product in Dirac-Kähler theory is not equivalent to ours.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
