Coulomb-quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex

Abstract

Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on 2D quantum problems and present complete treatment on the correspondence including the Schroedinger equation, eigenfunctions and eigenvalues, and the integrals of motion. We find only partial equivalence. The wavefunction correspondence is examined introducing local gauge transformation and the emergence of half-quantized vortex with the associated spin-half is established. Vortex structure of the electron proposed by us and the origin of charge are discussed in the present context. Outlook on the implications for QCD and hadron spectrum is outlined.

Stochasticity, topology, and spin

“…As an important consequence, the physical origin of spin acquires a radically new perspective. It necessitates re-examination of the roles of SED [14] and topology [15,19] in understanding spin.…”

“…Spin has been related with a topological invariant of half-quantized vortex in a recent geometric model of the electron [15,19]. For proton-spin de Rham period for a closed 3-form over a 3-cycle is identified to be a topological invariant [20].…”

“…In fact, Thomas work, nicely discussed by Tomonaga [6], has a profound observation on the parallel transport holonomy for spin of the electron highlighted recently [23]. Exact half-quantized vortex model of spin [15,19] seems to be applicable for massless particle; it is the mass term that requires attention for stochastic explanation.…”

“…We suggest that time τ = e 2 mc 3 corresponding to electron charge radius determines this distance. Topology and geometric model of electron [15,19] are naturally incorporated in this picture with a significant role of schotasticity.…”

“…A notable recent advancement is in the context of the origin of spin in SED [14]. On the other hand, we have explored topological origin of spin [15]. In SRF, it is possible to interpret the wave equations stochastically, hence the term "randon field".…”