Quantum field theory 1: Basics in mathematics and physics: a bridge between mathematicians and physicists

Eberhard Zeidler3540347623, 9783540347644, 9783540347620

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.” (SIAM Review 2008)

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Table of contents :
cover……Page 1
front-matter……Page 2
Contents……Page 12
00 Prologue……Page 24
01 Historical Introduction……Page 44
02 Phenomenology of the Standard Model for Elementary Particles……Page 102
03 The Challenge of Different Scales in Nature……Page 209
04 Analyticity……Page 230
05 A Glance at Topology……Page 247
06 Many-Particle Systems in Mathematics and Physics……Page 296
07 Rigorous Finite-Dimensional Magic Formulas of Quantum Field Theory……Page 343
08 Rigorous Finite-Dimensional Perturbation Theory……Page 514
09 Fermions and the Calculus for Grassmann Variables……Page 531
10 Infinite-Dimensional Hilbert Spaces……Page 537
11 Distributions and Green’s Functions……Page 590
12 Distributions and Physics……Page 683
13 Basic Strategies in Quantum Field Theory……Page 752
14 The Response Approach……Page 777
15 The Operator Approach……Page 824
16 Peculiarities of Gauge Theories……Page 887
17 A Panorama of the Literature……Page 916
Appendix A……Page 940
Epilogue……Page 963
References……Page 967
Index……Page 1003