# Quantum mechanics in multiply-connected spaces

@article{Ho1996QuantumMI, title={Quantum mechanics in multiply-connected spaces}, author={Vu Ho and Michael John Morgan}, journal={Journal of Physics A}, year={1996}, volume={29}, pages={1497-1510} }

This paper analyses quantum mechanics in multiply-connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular momentum. In particular, quantum mechanics in compactified Kaluza - Klein spaces is examined. These compactified spaces give rise to an additional angular momentum which can adopt half-integer values and therefore, may be identified with the intrinsic spin of a…

## 11 Citations

Quantum mechanics in multiply-connected spaces

- Physics
- 2007

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological…

J un 2 00 6 Quantum Mechanics in Multiply-Connected Spaces

- 2006

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological…

Constructing and Constraining Wave Functions for Identical Quantum Particles

- Physics
- 2016

I address the problem of explaining why wave functions for identical particles must be either symmetric or antisymmetric (the symmetry dichotomy) within two interpretations of quantum mechanics which…

FLUID STATE OF DIRAC QUANTUM PARTICLES

- 2018

In our previous works we suggest that quantum particles are composite physical objects endowed with the geometric and topological structures of their corresponding differentiable manifolds that would…

Identical Particles in Quantum Mechanics: Operational and Topological Considerations

- Physics, Mathematics
- 2016

This dissertation reports our investigation into the existence of anyons, which interpolate between bosons and fermions, in light of the Symmetrization Postulate, which states that only the two…

A FORMULATION OF SPIN DYNAMICS USING SCHRÖDINGER EQUATION

- 2019

In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space…

Bohmian Trajectories as the Foundation of Quantum Mechanics

- Physics
- 2009

Bohmian trajectories have been used for various purposes, including the numer- ical simulation of the time-dependent Schrodinger equation and the visualization of time-dependent wave functions. We…

General Relativistic Wormhole Connections from Planck-Scales and the ER = EPR Conjecture

- Physics, Computer ScienceEntropy
- 2020

These findings suggest that if the ER = EPR conjecture is valid, it can be extended to other different types of space–times and that gravity and space–time could be emergent physical quantities if the exchange of a virtual graviton between events can be considered connected by ER wormholes equivalent to entanglement connections.

An Intrinsic Theory of Quantum Mechanics: Progress in Field's Nominalistic Program, Part I

- Mathematics
- 2017

In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract…

Path Integrals in a Multiply-Connected Configuration Space (50 Years After)

- Mathematics, PhysicsFoundations of Physics
- 2021

The proposal made 50 years ago by Schulman (1968), Laidlaw & Morette-DeWitt (1971) and Dowker (1972) to decompose the propagator according to the homotopy classes of paths was a major breakthrough:…

## References

SHOWING 1-10 OF 13 REFERENCES

Twisted quantum fields in a curved space–time

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1978

Non-trivial space–time topology leads to the possibility of twisted fields viewed as cross sections of non-product vector bundles. For globally hyperbolic space–times twisted real and complex scalar…

A Path integral for spin

- Physics
- 1968

A path integral for spinning particles is developed. It is a one-particle theory, equivalent to the usual quantum mechanics. Our method employs a classical model for spin which is quantized by path…

Vacuum solutions for a twisted scalar field

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1978

The properties of the ground state of a classical self-interacting twisted scalar field on a two-dimensional Einstein cylinder are discussed. In particular there is a spontaneous breakdown of the…

Generalized orbital angular momentum and the n-fold degenerate quantum-mechanical oscillator: Part I. The twofold degenerate oscillator

- Physics
- 1960

Abstract An operational procedure is used to determine the eigenvalues and eigenfunctions for the quantum-mechanical twofold degenerate oscillator problem in polar coordinates. The procedure leads…

Single Valuedness of Wave Functions

- Physics
- 1962

The requirement that the quantal wave function be single-valued is examined in the light of two recent developments: The effect of a magnetic vector potential on a particle moving in a multiply…

GENERALIZED ORBITAL ANGULAR MOMENTUM AND THE N-FOLD DEGENERATE QUANTUM-MECHANICAL OSCILLATOR

- Physics
- 1960

A set of commuting generalized orbital angular momentum operators in n- dimensional polar coordinates is defined and their eigenvalues and simultaneous eigenfunctions determined by the use of results…

On the quantization of angular momentum

- Physics
- 1994

It is shown that when a hydrogen-like atom is treated as a two-dimensional system whose configuration space is multiply connected, then, in order to obtain the same energy spectrum as in the Bohr…

HYDROGEN ATOM AND RELATIVISTIC PI MESIC ATOM IN N SPACE DIMENSIONS

- Physics
- 1979

We derive in simple analytic closed form the eigenfunctions and eigenenergies for the hydrogen atom in N dimensions. A section is devoted to the specialization to one dimension. Comments are made on…

Gravitation, gauge theories and the early universe

- Physics
- 1989

I: Gravitation and Cosmology.- 1. Introduction to General Relativity.- 1. From Special Theory to General Theory.- 2. Einstein's Thought Experiment.- 3. Geometry or Geometries?.- 4. Riemannian…