Discrete Time from Quantum Physics

Details Discrete Time from Quantum Physics Discrete Time from Quantum Physics

1994-05-02

arxiv.org/abs/hep-th/9404193v2

Nucl.Phys. B428 (1994) 435-448

Physics

High Energy Physics

High Energy Physics - Theory

21 pages with 2 figures, SU-4240-579 (figures corrected in this version)

Scientific paper

10.1016/0550-3213(94)90207-0

't Hooft has recently developed a discretisation 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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