Finite Approximations to Quantum Physics: Quantum Points and their Bundles

Details Finite Approximations to Quantum Physics: Quantum Points and their Bundles Finite Approximations to Quantum Physics: Quantum Points and their Bundles

1993-10-04

arxiv.org/abs/hep-th/9310015v1

Nucl.Phys. B418 (1994) 477-493

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 8 figures on a uuencoded postscript file, DSF-T-29/93, INFN-NA-IV-29/93 and SU-4240-550

Scientific paper

10.1016/0550-3213(94)90527-4

There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively reproduce important topological features of continuum physics like winding numbers and fractional statistics, and that too often with just a few points. In this work, we develop the essential tools for doing quantum physics on posets. The poset approach to covering space quantization, soliton physics, gauge theories and the Dirac equation are discussed with emphasis on physically important topological aspects. These ideas are illustrated by simple examples like the covering space quantization of a particle on a circle, and the sine-Gordon solitons.

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