© 2006
Quantum Field Theory I: Basics in Mathematics and Physics
A Bridge between Mathematicians and Physicists
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© 2006
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. Upper-division undergraduates through faculty."
(M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007)
From the reviews:
"Quantum field theory combines relativity, quantum mechanics, and many-particle 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. Upper-division 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 six-volume 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)