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

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World Scientific, 1998 - Science - 266 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.
 

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Contents

Foundations
1
Logic and Set Theory
15
Group Duality Coherence and Cyclic Actions
31
A Quantum Net
53
Towards a Correspondence Principle for the Quantum Net
67
A Correspondence Principle for the Quantum Net
89
Dynamics I
131
Dynamics II
163
Comparisons Interpretations and Speculations
215
References
249
Index
257
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