Quantum Field Theory I: Basics in Mathematics and Physics

A Bridge between Mathematicians and Physicists
Softcover Nachdruck of the original 1. Auflage 2006
ISBN: 978-3-662-50094-1
Verlag: Springer

Buch, Englisch, 1051 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1591 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. This book presents the state of the art of scientific realization of Einstein's dream of a constructing a grand unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction).

Zielgruppe

Research

Autoren/Hrsg.

Zeidler, Eberhard

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Quantenphysik Teilchenphysik

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).