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Discrete time from quantum physics

Authors
Journal
Nuclear Physics B
0550-3213
Publisher
Elsevier
Publication Date
Volume
428
Identifiers
DOI: 10.1016/0550-3213(94)90207-0
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract '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.

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