Quantum Mechanics in Multiply-Connected Spaces

Abstract

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 ${\mathbb{R}}^{3N}$ to arbitrary Riemannian manifolds, and classifying the possible dynamics that arise. This approach provides a new understanding of the topological features of quantum theory, such as the symmetrization postulate for identical particles. For our analysis we employ wave functions on the universal covering space of the configuration space.

45 pages LaTeX, no figures; v2 some extensions

References in corpus (9)

• Quantum Equilibrium and the Origin of Absolute Uncertainty
• On Spontaneous Wave Function Collapse and Quantum Field Theory
• Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
• On the Global Existence of Bohmian Mechanics
• A Survey on Bohmian Mechanics
• Simple Proof for Global Existence of Bohmian Trajectories
• Are All Particles Real?
• Topological Factors Derived From Bohmian Mechanics
• Quantum mechanics in multiply connected spaces

Cited by in corpus (13)

• On the Role of Density Matrices in Bohmian Mechanics
• Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function
• Topological Factors Derived From Bohmian Mechanics
• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• Coherent states for the quantum mechanics on a torus
• The Analogue of Bohm-Bell Processes on a Graph
• Bohmian Trajectories for Hamiltonians with Interior-Boundary Conditions
• Fermionic Wave Functions on Unordered Configurations
• Emergent quantum mechanics of the event-universe, quantization of events via Denrographic Hologram Theory
• Bohmian Mechanics at Space-Time Singularities. I. Timelike Singularities
• Interior-Boundary Conditions for Schrodinger Operators on Codimension-1 Boundaries
• Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles
• Constructing and Constraining Wave Functions for Identical Quantum Particles