Quantum Field Theory I: Basics in Mathematics and Physics

A Bridge between Mathematicians and Physicists

  • Authors
  • Eberhard Zeidler

Table of contents

  1. Front Matter
    Pages I-XXIV
  2. Introduction

    1. Eberhard Zeidler
      Pages 1-20
    2. Eberhard Zeidler
      Pages 21-79
    3. Eberhard Zeidler
      Pages 189-209
  3. Basic Techniques in Mathematics

    1. Eberhard Zeidler
      Pages 211-227
    2. Eberhard Zeidler
      Pages 229-277
    3. Eberhard Zeidler
      Pages 279-325
    4. Eberhard Zeidler
      Pages 499-515
    5. Eberhard Zeidler
      Pages 517-522
    6. Eberhard Zeidler
      Pages 523-575
    7. Eberhard Zeidler
      Pages 577-670
    8. Eberhard Zeidler
      Pages 671-740
  4. Heuristic Magic Formulas of Quantum Field Theory

    1. Eberhard Zeidler
      Pages 741-765
    2. Eberhard Zeidler
      Pages 767-813
    3. Eberhard Zeidler
      Pages 815-877
    4. Eberhard Zeidler
      Pages 879-907
    5. Eberhard Zeidler
      Pages 909-946
  5. Back Matter
    Pages 947-1051

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. Upper-division undergraduates through faculty."

(M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007)


Distribution Finite Hilbert space Operator Topology Variable functional analysis general relativity linear optimization mathematical physics mathematics model particle physics quantum field theory statistical mechanics

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-34764-4
  • Copyright Information Springer Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-34762-0
  • Online ISBN 978-3-540-34764-4
  • About this book