On the ultraviolet behaviour of quantum fields over noncommutative manifolds

Abstract

By exploiting the relation between Fredholm modules and the Segal-Shale-Stinespring version of canonical quantization, and taking as starting point the first-quantized fields described by Connes' axioms for noncommutative spin geometries, a Hamiltonian framework for fermion quantum fields over noncommutative manifolds is introduced. We analyze the ultraviolet behaviour of second-quantized fields over noncommutative 3-tori, and discuss what behaviour should be expected on other noncommutative spin manifolds.

10 pages, RevTeX version, a few references added

References in corpus (2)

• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• On summability of distributions and spectral geometry

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