Quanta, Logic and Spacetime: Variations on Finkelstein's Quantum Relativity
World Scientific, 12 mars 1998 - 284 pages
In this highly interesting monograph, a brief account of Finkelstein's approach to quantum theory and some of its ramifications is given. Specifically, his suggestion that some sort of quantum-set-like structure should underlie our macroscopic perception of spacetime is developed to the point where a fair slice of fundamental physics (for a massless world) may be formally derived in an elementary fashion from the ground up. In detail, a model of what Finkelstein has dubbed a “quantum net”, in conjunction with a carefully and extensively articulated correspondence principle, gives rise to the standard Lagrangians for: massless Dirac fermions, general relativity, and Yang-Mills fields for the gauge groups, U(1) x SU(2), and SU(3). These Lagrangians emerge replete with (Feynman) gauge-fixing terms and ghost fields, and a chiral breaking mechanism in the case of SU(2). The results are interpreted in the light of the Standard Model.
Contents: FoundationsLogic and Set TheoryGroup DualityCoherence and Cyclic ActionsA Quantum NetTowards a Correspondence Principle for the Quantum NetA Correspondence Principle for the Quantum NetDynamics IDynamics IIComparisons, Interpretations and Speculations
Readership: Mathematicians and physicists.
keywords:Relativity;Quantum Theory;Quantum Logic;Spacetime;Elementary Particles
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2 Logic and Set Theory
3 Group Duality Coherence and Cyclic Actions
4 A Quantum Net
5 Towards a Correspondence Principle for the Quantum Net
6 A Correspondence Principle for the Quantum Net