ON THE ULTRAVIOLET BEHAVIOR OF QUANTUM FIELDS OVER NONCOMMUTATIVE MANIFOLDS
- 30 March 1999
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A
- Vol. 14 (8) , 1305-1323
- https://doi.org/10.1142/s0217751x99000671
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.Keywords
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