A purely geometrical Aharonov-Bohm effect

This presentation builds up on our work in progress [1] and our previous work [2][3][4] that delved into the quantum aspects of motion in a punctured plane. The removal of the classical singularity in this context is attributed to the regularization provided by 2-D covariant affine integral quantization. In addition to introducing a repulsive centrifugal-like potential through this process, we also uncover vector and scalar potentials whose magnitude is directly proportional to the Planck constant. We study the conditions that give rise to the vector potential, which bears a striking resemblance to the field produced by an infinitely thin solenoid, oriented orthogonally to the punctured plane at the point of removal.

1. " A purely geometrical Aharonov-Bohm effect”, JP Gazeau, T Koide, R Murenzi, and Aidan Hayle Zlotak, work in progress.

2. "2-D covariant affine integral quantization (s)", JP Gazeau, T Koide, R Murenzi, Advances in Operator Theory 5 (3), 901-935, 2020

3. "1D & 2D Covariant Affine Integral Quantizations”, Geometric Methods in Physics. XXXVI Workshop 2017 Trends in Mathematics, 39–45, Springer Nature Switzerland AG 2019

4. “"More quantum centrifugal effect in rotating frame” JP Gazeau, T Koide, R Murenzi - Europhysics Letters, 201