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量子、逻辑与时空 QUANTA, LOGIC AND SPACETIME (2ND EDITION)

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  分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者: S. A. Selesnick著

出 版 社: Penguin

出版时间: 2003-12-1字数:版次: 1页数: 464印刷时间: 2003/11/01开本:印次: 1纸张: 胶版纸I S B N : 9789812386915包装: 挂图内容简介

In this expanded edition of Quanta, Logic and Spacetime, 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, including gravity. The logic of this process is now subject to greater formal rigor than was possible in the first edition, and the central thesis — that quantum physics at a fundamental level may itself be realized as a species of quantum computation — is strongly underscored.

目录

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 HopfAlgebras

3.1.1 Algebras

3.1.2 Coalgebras

3.1.3 Bialgebras and HopfAlgebras

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 amd 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 (n,C) to Z

3.2.2 Condensation and Coherence

3.2.3 Quantizing Cycles: from 7/n to (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

5.10rthologic 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 Isham 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 SequentCalculus for Quantum Resources

6.3 Intuitionistic Orthologic and GQ

……

Part III The Plenum

References

Citation Index

Notational index and Glossary

Subject Index

 
 
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