Quanta, Logic and Spacetime: Variations on Finkelstein's Quantum Relativity

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World Scientific, 12 mars 1998 - 284 pages
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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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Table des matières

1 Foundations
1
2 Logic and Set Theory
15
3 Group Duality Coherence and Cyclic Actions
31
4 A Quantum Net
53
5 Towards a Correspondence Principle for the Quantum Net
67
6 A Correspondence Principle for the Quantum Net
89
7 Dynamics I
131
8 Dynamics II
163
9 Comparisons Interpretations and Speculations
215
References
249
Index
257
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À propos de l'auteur (1998)

S A Selesnick (University of Missouri-St. Louis)

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