English

Quantum Mechanics On Spaces With Finite Fundamental Group

Quantum Physics 2007-05-23 v1 General Relativity and Quantum Cosmology

Abstract

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of observables \O\O to the commutant of the algebra generated by deck-transformations. We apply standard superselection principles and construct the corresponding sectors. We emphasize the relevance of all sectors and not just the abelian ones.

Keywords

Cite

@article{arxiv.quant-ph/9508011,
  title  = {Quantum Mechanics On Spaces With Finite Fundamental Group},
  author = {Domenico Giulini},
  journal= {arXiv preprint arXiv:quant-ph/9508011},
  year   = {2007}
}

Comments

40 Pages, Plain-TeX, no figures

R2 v1 2026-07-22T20:00:26.450Z