05018nam 2200661Ia 450 991078211710332120200520144314.01-281-93541-79786611935412981-279-493-X(CKB)1000000000537808(EBL)1681688(OCoLC)879025526(SSID)ssj0000231138(PQKBManifestationID)11947245(PQKBTitleCode)TC0000231138(PQKBWorkID)10198692(PQKB)11505391(MiAaPQ)EBC1681688(WSP)00005421(Au-PeEL)EBL1681688(CaPaEBR)ebr10255933(CaONFJC)MIL193541(PPN)164634053(EXLCZ)99100000000053780820030925d2003 uy 0engur|n|---|||||txtccrQuanta, logic and spacetime[electronic resource] /S.A. Selesnick2nd ed.River Edge, NJ World Scientificc20031 online resource (487 p.)Description based upon print version of record.981-238-691-2 Includes bibliographical references (p. 429-441) and indexes.Contents ; Part I Preliminaries ; 1. Foundations ; 1.1 Physics without Objects ; 1.2 Observables ; 1.3 Finite Dimensional Heuristics ; 2. Quantum Sets ; 2.1 Logics and Lattices ; 2.2 Some First-order Quantum Aggregates ; 2.2.1 Finite Products ; 2.2.2 Sequences ; 2.2.3 Sets2.2.4 Sibs 2.3 Quantum Set Theory ; 3. Group Duality Coherence and Cyclic Actions ; 3.1 The Duality of Groups and Hopf Algebras ; 3.1.1 Algebras ; 3.1.2 Coalgebras ; 3.1.3 Bialgebras and Hopf Algebras ; 3.1.4 The Additive Affine Group ; 3.1.5 Finite Group Algebras3.1.6 Topological Hopf and Coalgebras 3.1.7 The Algebra of Representative Functions on a Compact Group ; 3.1.8 Tensor Symmetric and Exterior Algebras ; 3.1.9 The Universal Enveloping Algebra of a Lie Algebra ; 3.2 Quantum Versions of Cyclic Groups3.2.1 Quantum Permutations: from SI(n C) to Zn 3.2.2 Condensation and Coherence ; 3.2.3 Quantizing Cycles: from Zn to SI(n C) ; Part II Computational Paradigms ; 4. Natural Deduction ; 4.1 Natural Deduction for a Minimal System ; 4.2 The Curry-Howard Isomorphism4.3 The Gentzen Sequent Calculus 5. Quantum Logic ; 5.1 Orthologic and its Model Theory ; 5.1.1 Orthologic as a Deductive System ; 5.1.2 Modal Logic and Kripke Models ; 5.1.3 A Modal Translation Theorem ; 5.1.4 The Implication Problem and Orthomodular Logic5.1.5 Orthomodular Foundations for Quantum MechanicsIn this expanded edition of <i>Quanta, Logic and Spacetime</i>, the logical base is greatly broadened and quantum-computational aspects of the approach are brought to the fore. The first two parts of this edition may indeed be regarded as providing a self-contained and logic-based foundation for - and an introduction to - the enterprise known as quantum computing. The rest of the work takes on the task (as in the first edition) of computing from first principles certain dynamical expressions which turn out to compare favorably with the Lagrangian densities of the (massless) Standard Model, iQuantum theorySpecial relativity (Physics)Quantum theory.Special relativity (Physics)530.12Selesnick S. A(Stephen Allan)626249MiAaPQMiAaPQMiAaPQBOOK9910782117103321Quanta, logic and spacetime1218877UNINA