Mathematics of quantization and quantum fields / Jan Dereziński, University of Warsaw, Poland, Christian Gérard, Universite de Paris-Sud, France.

Format:

Book

Author/Creator:

Dereziński, Jan, 1957- author.

Gérard, Christian, 1960- author.

Series:

Cambridge monographs on mathematical physics.

Cambridge monographs on mathematical physics

Language:

English

Subjects (All):

Geometric quantization.

Quantum theory--Mathematics.

Quantum theory.

Physical Description:

1 online resource (xii, 674 pages) : digital, PDF file(s).

Other Title:

Mathematics of Quantization & Quantum Fields

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Language Note:

English

Summary:

Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, like tensors, algebras, Fock spaces, and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in departments of mathematics and physics.

Contents:

Introduction

1. Vector spaces

2. Operators in Hilbert spaces

3. Tensor algebras

4. Analysis in L2(Rd)

5. Measures

6. Algebras

7. Anti-symmetric calculus

8. Canonical commutation relations

9. CCR on Fock spaces

10. Symplectic invariance of CCR in finite dimensions

11. Symplectic invariance of the CCR on Fock spaces

12. Canonical anti-commutation relations

13. CAR on Fock spaces

14. Orthogonal invariance of CAR algebras

15. Clifford relations

16. Orthogonal invariance of the CAR on Fock spaces

17. Quasi-free states

18. Dynamics of quantum fields

19. Quantum fields on space-time

20. Diagrammatics

21. Euclidean approach for bosons

22. Interacting bosonic fields.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-107-23471-9

1-107-33563-9

1-107-33242-7

1-107-32670-2

1-107-33314-8

1-107-33646-5

1-107-33480-2

0-511-89454-6

OCLC:

843192059