Mathematics of Quantization and Quantum Fields

1. Auflage 2014
ISBN: 978-1-107-01111-3
Verlag: Cambridge University Press

Buch, Englisch, 688 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1347 g

Reihe: Cambridge Monographs on Mathematical Physics

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.

Autoren/Hrsg.

Derezi Ski, Jan

Derezinski, Jan

G. Rard, Christian

Gerard, Christian

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik

Inhaltsverzeichnis

Preface; 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; Subject index; Symbols index.

Über Autor(innen)

Derezinski, Jan
Jan Derezinski is a Professor in the Faculty of Physics at the University of Warsaw. His research interests cover various aspects of quantum physics and quantum field theory, especially from the rigorous point of view.

G. Rard, Christian
Christian Gérard is a Professor in the Département de Mathématiques at the Université Paris-Sud. He was previously Directeur de Recherche at the CNRS (Centre National de la Recherche Scientifique). His research interests are the spectral and scattering theory in non-relativistic quantum mechanics and in quantum field theory.

Jan Derezinski is a Professor in the Faculty of Physics at the University of Warsaw. His research interests cover various aspects of quantum physics and quantum field theory, especially from the rigorous point of view.

Christian Gérard is a Professor in the Département de Mathématiques at the Université Paris-Sud. He was previously Directeur de Recherche at the CNRS (Centre National de la Recherche Scientifique). His research interests are the spectral and scattering theory in non-relativistic quantum mechanics and in quantum field theory.