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 Sets -- 2.2.4 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 Algebras -- 3.1.6 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 Groups -- 3.2.1 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 Isomorphism -- 4.3 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 Logic -- 5.1.5 Orthomodular Foundations for Quantum Mechanics -- 5.2 Quantum Logic Proper: Hilbert Models -- 5.2.1 Observables and States for Hilbert Lattices -- 5.2.2 The Kochen-Specker Theorem a les lsham and Butterfield -- 5.3 Critique of Quantum Logic -- 6. The Computational Resources of Quantum Logic -- 6.1 An Orthological Toy -- 6.2 GQ: A Minimal Intuitionisitic Propositional Sequent Calculus for Quantum Resources -- 6.3 Intuitionistic Orthologic and GQ.

6.3.1 A Translation Theorem -- 6.3.2 The Model Category -- 6.3.3 A Model of Computation and the Emergence of the Qubit -- 6.3.4 Quantum Duplication as Entanglement -- 6.4 Quantum Computing in Classical Time: An Algebraic Model -- 6.5 Conclusions -- Part III The Plenum -- 7. A Quantum Net -- 7.1 Symmetries of the Qubit -- 7.2 A Superconducting Quantum Net -- 7.2.1 Some Remarks on Types and Reductions -- 7.3 A Geometrical Approach to the Net -- 8. Towards a Correspondence Principle for the Quantum Net -- 8.1 Vectors -- 8.2 Transport Curves and a little Chenism -- 9. A Correspondence Principle for the Quantum Net -- 9.1 Spinor Duality -- 9.2 Variation Derivation and the Dirac Maps -- 9.3 The A Operators -- 9.4 The Real Subspace Frame Choices and Dirac Matrices -- 9.4.1 General Transformations -- 9.5 The Correspondence Principle -- 10. Dynamics I -- 10.1 Dynamic Transport and the Lagrangian -- 10.2 Problems with the Dirac Operator -- 10.3 Feynman Path Integral and Field Equations -- 10.3.1 Solving the Weyl Equations by (Quantum) Thinking! -- 11. Dynamics II -- 11.1 The Defect's New Clothes -- 11.2 Dynamic Transport and the Lagrangian Revisited -- 11.2.1 The Interaction Term -- 11.2.2 The Kinetic Term -- 11.2.3 Ghosts -- 11.3 Resolution and Rescaling -- 12. Comparisons Interpretations and Speculations -- 12.1 An Abbreviated Sketch of the Standard Model -- 12.2 Asymptotic Freedom and Grand Unification -- 12.3 Superconduction and Electroweak Unification -- 12.4 Long Distance Topological Implications -- 12.5 Quantization Connections and Loop Quantum Gravity -- 12.6 Outlook -- References -- Citation Index -- Notational Index and Glossary -- Subject Index.