Q. An algebraic language for quantum-spacetime topology

Journal Article · Sun Mar 31 23:00:00 EST 1991 · International Journal of Theoretical Physics; (United States)

DOI:https://doi.org/10.1007/BF00672892· OSTI ID:5363241

Finkelstein, D; Hallidy, W H ^[1]

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1. Georgia Inst. of Tech., Atlanta (United States)

The authors 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 {contains} CQ {contains} C. Q predicates are the rays in a Grassmann double algebra of extensors, where CQ predicates are the subspaces of a Hilbert 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.

• OSTI ID: 5363241
• Journal Information: International Journal of Theoretical Physics; (United States), Journal Name: International Journal of Theoretical Physics; (United States) Vol. 30:4; ISSN 0020-7748; ISSN IJTPB
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BANACH SPACE
HILBERT SPACE
INVARIANCE PRINCIPLES
MATHEMATICAL LOGIC
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
QUANTUM MECHANICS
SET THEORY
SPACE
SPACE-TIME
TOPOLOGY