Modular Momentum of the Aharonov-Bohm Effect on Noncommutative Lattices

TL;DR

This paper explores the relationship between modular momentum in the Aharonov-Bohm effect and noncommutative lattices using noncommutative geometry and theta quantization, revealing a new mathematical equivalence.

Contribution

It establishes a novel equivalence between modular momentum and noncommutative lattices in the context of the Aharonov-Bohm effect using noncommutative geometry techniques.

Findings

Demonstrates the equivalence via theta quantization

Links modular momentum to noncommutative lattice structures

Provides a new mathematical framework for the effect

Abstract

Based on the technique of noncommutative geometry, it is shown that, by means of the concept of the theta quantization, there is an equivalence between the notion of the modular momentum of the Aharonov-Bohm effect and the notion of a noncommutative lattice over a circle poset.