# Quantum mechanics in multiply-connected spaces

@article{Duerr2007QuantumMI, title={Quantum mechanics in multiply-connected spaces}, author={Detlef Duerr and Sheldon Goldstein and James Taylor and Roderich Tumulka and Nino Zangh{\'i}}, journal={Journal of Physics A}, year={2007}, volume={40}, pages={2997-3031} }

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 factors. We do this in the context of Bohmian mechanics, a quantum theory without observers from which the quantum formalism can be derived. What we do can be regarded as generalizing the Bohmian dynamics on to arbitrary Riemannian manifolds, and classifying the possible dynamics that arise. This…

## 16 Citations

Topological Factors Derived from Bohmian Mechanics

- Physics, Mathematics
- 2006

AbstractWe derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space
$$ \mathcal{Q}. $$ These include nonabelian factors corresponding to what…

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…

The Analogue of Bohm-Bell Processes on a Graph

- Physics
- 2006

Abstract Bohm–Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes Q t generalizing in a natural way both Bohm's dynamical system in configuration…

Fermionic Wave Functions on Unordered Configurations

- Mathematics, Physics
- 2014

Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations. Leinaas and Myrheim proposed how a fermionic wave function can…

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…

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…

Bohmian mechanics at space–time singularities: II. Spacelike singularities

- Physics
- 2010

We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space–time containing a spacelike singularity. As an example of such a…

Bohmian mechanics at space–time singularities. I. Timelike singularities

- Physics, MathematicsJournal of Geometry and Physics
- 2019

Abstract We develop an extension of Bohmian mechanics to a curved background space–time containing a singularity. The present paper focuses on timelike singularities. We use the naked timelike…

Density dynamics in some quantum systems

- Physics
- 2013

The quantum domain behavior of classical nonintegrable systems is well-understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the…

New Type of Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories

- Physics
- 2015

We propose a novel type of Hamiltonians for quantum eld theories. They are mathematically well-dened (and in particular, ultraviolet nite) without any ultraviolet cut-o such as smearing out the…

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