1994/04/30 by A. P. Balachandran, L. Chandar · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1016/0550-3213(94)90207-0
published as Nucl.Phys. B428 (1994) 435-448 · 21 pages with 2 figures, SU-4240-579 (figures corrected in this version)
arxiv created 1994/05/03 · openalex publication_date 1994/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
't Hooft has recently developed a discretization of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum with single-valued equations of motion in classical physics, but with multiple-valued Hamiltonians. Their time displacements in quantum theory are therefore obliged to be discrete. Classical models on smooth spatial manifolds are also constructed with the property that spatial displacements can be implemented only in discrete steps in quantum theory. All these models show that quantization can profoundly affect classical topology.