Quantum Field Theory I: Basics in Mathematics and Physics
A Bridge between Mathematicians and Physicists
Authors: Zeidler, Eberhard
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 About this book

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown 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 is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction).
From the reviews:
"… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from other books on quantum field theory in its greater emphasis on the interaction of physics with mathematics. … an impressive work of scholarship."
(William G. Faris, SIAM Review, Vol. 50 (2), 2008)
"… it is a fun book for practicing quantum field theorists to browse, and it may be similarly enjoyed by mathematical colleagues. Its ultimate value may lie in encouraging students to enter this challenging interdisciplinary area of mathematics and physics. Summing Up: Recommended. Upperdivision undergraduates through faculty."
(M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007)
 About the authors

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 HalbachStiftung.
The author wrote the following books.
(a) E. Zeidler, Nonlinear Functional Analysis and its Applications, Vols. IIV,
Springer Verlag New York, 19841988 (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,
SpringerVerlag, New York, 1995.(d) E. Zeidler, Oxford Users' Guide to Mathematics, Oxford University Press, 2004
(translated from German).  Reviews

From the reviews:
"Quantum field theory combines relativity, quantum mechanics, and manyparticle physics to provide a theoretical basis for the most fundamental understanding of our universe. … it is a fun book for practicing quantum field theorists to browse, and it may be similarly enjoyed by mathematical colleagues. Its ultimate value may lie in encouraging students to enter this challenging interdisciplinary area of mathematics and physics. Summing Up: Recommended. Upperdivision undergraduates through faculty." (M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007)
"This is the first volume of a six volume book on quantum field theory. … The main object is to explain mathematics for students or researchers in physics how to use them, and to show students and researchers in mathematics how to use them, and to show students and researchers in mathematics how to use mathematics in physics. Translations of different languages used by mathematicians and physicists for the same mathematical objects are also presented." (Akira Asada, Zentralblatt MATH, Vol. 1124 (1), 2008)
"This book on quantum field theory, consisting of over a thousand pages, is the first volume of a projected sixvolume series. It alone has seventeen chapters and an appendix … . The appendix covers notation, units, and dimensional analysis. … Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from other books on quantum field theory in its greater emphasis on the interaction of physics with mathematics. … an impressive work of scholarship." (William G. Faris, SIAM Review, Vol. 50 (2), 2008)
“Volume I is divided in three parts. Part 1 has an introductory nature. … Part II accompanies the reader through a forest of basic techniques in mathematics. … In Part III, Zeidler presents the essential available information on heuristic magic formulas of quantum field theory. … The presentation of the material is clear. … For a scholar aiming to work in quantum field theory … Zeidler can be a reference text. … Mathematicians can find a list of topics who are still waiting rigorous treatments.” (Paolo Maria Mariano, Meccanica, Vol. 46, 2011)
 Table of contents (18 chapters)


Prologue
Pages 120

Historical Introduction
Pages 2179

Phenomenology of the Standard Model for Elementary Particles
Pages 81187

The Challenge of Different Scales in Nature
Pages 189209

Analyticity
Pages 211227

Table of contents (18 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Quantum Field Theory I: Basics in Mathematics and Physics
 Book Subtitle
 A Bridge between Mathematicians and Physicists
 Authors

 Eberhard Zeidler
 Copyright
 2006
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783540347644
 DOI
 10.1007/9783540347644
 Hardcover ISBN
 9783540347620
 Softcover ISBN
 9783662500941
 Edition Number
 1
 Number of Pages
 XXIV, 1051
 Topics