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 behavior of second-quantized fields over noncommutative three-tori, and discuss what behavior should be expected on other noncommutative spin manifolds.
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