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      ON THE ULTRAVIOLET BEHAVIOR OF QUANTUM FIELDS OVER NONCOMMUTATIVE MANIFOLDS

      1 , 2
      International Journal of Modern Physics A
      World Scientific Pub Co Pte Lt

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          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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          Most cited references15

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          Non-commutative differential geometry

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            Projective modules over higher-dimensional noncommutative tori

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              Principe d'Oka,K-th�orie et syst�mes dynamiques non commutatifs

              J. B. Bost (1990)
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                Author and article information

                Journal
                International Journal of Modern Physics A
                Int. J. Mod. Phys. A
                World Scientific Pub Co Pte Lt
                0217-751X
                1793-656X
                January 25 2012
                March 30 1999
                January 25 2012
                March 30 1999
                : 14
                : 08
                : 1305-1323
                Affiliations
                [1 ]Department of Mathematics, Universidad de Costa Rica, San Pedro 2060, Costa Rica, USA
                [2 ]Department of Physics, Universidad de Costa Rica, San Pedro 2060, Costa Rica, USA
                Article
                10.1142/S0217751X99000671
                ae72ccb7-5bf0-4552-b095-5f5c51509702
                © 1999
                History

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