International Journal of Theoretical Physics

, Volume 30, Issue 4, pp 463–486 | Cite as

Q an algebraic language for quantum-spacetime topology

  • David Finkelstein
  • W. H. Hallidy


We propose a third physical logics. The first was classical (C) logics with commutative distributive AND and OR. The second is commutative quantum (CQ) logics, with commutative nondistributive AND and OR. The third logics, Q, has noncommutative nondistributive AND and OR; Q⊃CQ⊃C. Q predicates are the rays in a Grassmann double algebra of extensors, where CQ predicates are the subspaces of a Hubert space. The AND and OR of Q are projectively represented by Grassmann's progressive and regressive products. Q supports a quantum set theory appropriate to quantum topology. Here Q is applied to a toy theory of the topology of time. It preserves translational invariance and replaces singular delta-function propagators by finite Gaussians.


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • David Finkelstein
    • 1
  • W. H. Hallidy
    • 2
  1. 1.School of PhysicsGeorgia Institute of TechnologyAtlanta
  2. 2.Georgia Tech Research InstituteGeorgia Institute of TechnologyAtlanta

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