Quantum mechanics in multiply-connected spaces

Detlef Dürr, Sheldon Goldstein, James Taylor, Roderich Tumulka, Nino Zanghì
2007 Journal of Physics A: Mathematical and Theoretical  
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
more » ... 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.
doi:10.1088/1751-8113/40/12/s08 fatcat:xxcmswn2f5ekrh65cwmrigdloy