Path Integral in Modular Space

• URL: http://arxiv.org/abs/2002.01604v1
• Date: Wed, 5 Feb 2020 02:02:11 GMT
• Title: Path Integral in Modular Space
• Authors: Yigit Yargic
• Abstract summary: We construct a Feynman path integral for the quantum harmonic oscillator in a modular polarization. This path integral is endowed with novel features such as a new action, winding modes, and an Aharonov-Bohm phase. We propose a prescription analogous to the Legendre transform, which can be applied generally to the Hamiltonian of a variety of physical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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