论文标题
模块空间中的路径积分
Path Integral in Modular Space
论文作者
论文摘要
模块化空间是基于Aharonov的模块化变量并具有丰富的几何结构的希尔伯特空间极化的家族。我们在这里逐步构建，这是模块化极化中量子谐波振荡器的Feynman路径积分。这种模块化路径积分具有新的功能，例如新作用，绕组模式和Aharonov-Bohm相。它的鞍点是叠加状态的序列，它们具有与量子参考框架的理解相符的非古典概念。模块化路径积分中发现的动作可以理解为生活在紧凑的相空间上，并且具有一组新的对称性。最后，我们提出了类似于Legendre Transform的处方，该处方通常可以应用于各种物理系统的Hamiltonian，以产生类似的模块化作用。
The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic oscillator in a modular polarization. This modular path integral is endowed with novel features such as a new action, winding modes, and an Aharonov-Bohm phase. Its saddle points are sequences of superposition states and they carry a non-classical concept of locality in alignment with the understanding of quantum reference frames. The action found in the modular path integral can be understood as living on a compact phase space and it possesses a new set of symmetries. Finally, we propose a prescription analogous to the Legendre transform, which can be applied generally to the Hamiltonian of a variety of physical systems to produce similar modular actions.
