Mathematics of Quantization and Quantum Fields

Jan Dereziński; Christian Gérard

doi:10.1017/CBO9780511894541

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Mathematics of Quantization and Quantum Fields

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Contents

Frontmatter
pp i-viii

Contents
pp ix-xii

Introduction
pp 1-7

1 - Vector spaces
pp 8-35

2 - Operators in Hilbert spaces
pp 36-56

3 - Tensor algebras
pp 57-91

4 - Analysisin L2 (ℝd)
pp 92-110

5 - Measures
pp 111-141

6 - Algebras
pp 142-158

7 - Anti-symmetric calculus
pp 159-172

8 - Canonical commutation relations
pp 173-211

9 - CCR on Fock space
pp 212-238

10 - Symplectic invariance of CCR in finite-dimensions
pp 239-265

11 - Symplectic invariance of the CCR on Fock spaces
pp 266-312

12 - Canonical anti-commutation relations
pp 313-336

13 - CAR on Fock spaces
pp 337-350

14 - Orthogonal invariance of CAR algebras
pp 351-367

15 - Clifford relations
pp 368-385

16 - Orthogonal invariance of the CAR on Fock spaces
pp 386-422

17 - Quasi-free states
pp 423-474

18 - Dynamics of quantum fields
pp 475-511

19 - Quantum fields on space-time
pp 512-554

20 - Diagrammatics
pp 555-604

21 - Euclidean approach for bosons
pp 605-640

22 - Interacting bosonic fields
pp 641-660

References
pp 661-667

Symbols index
pp 668-670

Subject index
pp 671-674

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