Quantum Field Theory I: Basics in Mathematics and Physics

A Bridge between Mathematicians and Physicists
1..Auflage 2006. Corr. 2. printing 2009
ISBN: 978-3-540-34762-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 1052 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1753 g

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Zielgruppe

Research

Autoren/Hrsg.

Zeidler, Eberhard

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Geometrie
• Naturwissenschaften Astronomie Astrophysik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Astrophysik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik

Inhaltsverzeichnis

Prologue.- Historical Introduction.- Phenomenology of the Standard Model for Elementary Particles.- The Challenge of Different Scales in Nature.- Basic Techniques in Mathematics.- Analyticity.- A Glance at Topology.- Many-Particle Systems in Mathematics and Physics.- Rigorous Finite-Dimensional Magic Formulas of Quantum Field Theory.- Rigorous Finite-Dimensional Perturbation Theory.- Fermions and the Calculus for Grassmann Variables.- Infinite-Dimensional Hilbert Spaces.- Distributions and Green’s Functions.- Distributions and Physics.- Heuristic Magic Formulas of Quantum Field Theory.- Basic Strategies in Quantum Field Theory.- The Response Approach.- The Operator Approach.- Peculiarities of Gauge Theories.- A Panorama of the Literature.

Über Autor(innen)

Prof. Dr. Dr. h.c. Eberhard Zeidler works at the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany). In 1996 he was one of the founding directors of this institute. He is a member of the Academy of Natural Scientists Leopoldina. In 2006 he was awarded the "Alfried Krupp Wissenschaftspreis" of the Alfried Krupp von Bohlen und Halbach-Stiftung.

The author wrote the following books.

(a) E. Zeidler, Nonlinear Functional Analysis and its Applications, Vols. I-IV,
Springer Verlag New York, 1984-1988 (third edition 1998).

(b) E. Zeidler, Applied Functional Analysis, Vol. 1:
Applications to Mathematical Physics, 2nd edition, 1997, Springer Verlag, New York.

(c) E. Zeidler, Applied Functional Analysis, Vol. 2:
Main Principles and Their Applications,
Springer-Verlag, New York, 1995.

(d) E. Zeidler, Oxford Users' Guide to Mathematics, Oxford University Press, 2004
(translated from German).