# 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

- 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

- 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…

Fermionic Wave Functions on Unordered Configurations

- 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…

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, Mathematics
- 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

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

- Mathematics
- 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…

## References

SHOWING 1-10 OF 33 REFERENCES

Quantum mechanics in multiply-connected spaces

- Physics
- 1996

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…

Quantum mechanics and field theory on multiply connected and on homogeneous spaces

- Physics
- 1972

The basic framework for discussing quantum mechanics on multiply connected spaces is presented using the covering space concept. The theorem of Laidlaw and DeWitt is rederived and extended to the…

Topological Factors Derived from Bohmian Mechanics

- 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…

Quantum mechanics of relativistic particles in multiply connected spaces and the Aharonov-Bohm effect

- Physics
- 1991

The authors consider the motion of free relativistic particles in multiply connected spaces. They show that if one of the spatial dimensions has the topology of a circle then the D-dimensional…

The Role of Topology in Classical and Quantum Physics

- Physics
- 1992

An Elementary Introduction to Algebraic Topology..- Topological Methods in Classical Field Theory..- Inequivalent Quantizations in Multiply Connected Spaces. Braid Groups and Anyons..- Topics in…

On spontaneous wave function collapse and quantum field theory

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2006

One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous…

Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory

- Physics
- 2003

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schrödinger's equation into a completely coherent physical theory. It describes a world in which particles move in a…

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…

A survey of Bohmian mechanics

- Physics
- 1995

SummaryBohmian mechanics is the most naively obvious embedding imaginable of Schrödinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a…

On the global existence of Bohmian mechanics

- Mathematics
- 1995

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity…