## Quanta, Logic, and Spacetime: Variations on Finkelstein's Quantum RelativityIn 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 |

249 | |

257 | |

### Other editions - View all

Quanta, Logic and Spacetime: Variations on Finkelstein's Quantum Relativity S A Selesnick Limited preview - 1998 |

### Common terms and phrases

act of injecting adjoint algebra structure amplitude analog appropriate associated assume bispinor bosons chapter choice chrononic classical coalgebra commutative complex component contraction correspondence principle counit defect defined degree of resolution denotes diagram Dirac maps dual dynamical effect eigenvalue elements EndW expression fermions field finite dimensional Finkelstein frame function gauge geometrical Hilbert space Hopf algebra infinitesimal initial action vectors initial acts initial vectors injectors interaction term interpretation isomorphism Lagrangian last equation lattice Lie algebra line bundle linear map macroscopic macroscopic experimenters manifold massless matrix Maxwell-Boltzmann phase namely notation obtain operator pair parallel transport permutations quantum logic replaced represent representation result reticular right hand side second quantized selective acts Selesnick sequence side of equation spacetime spinor spontaneous symmetry breaking subspaces superconduction superconductor superposition symmetry breaking tion topological trace transformations transition transport trivial underlying vacuum variation vector space Weyl Weyl equations yields