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In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction.
Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure.
The book is arranged in four sections, devoted to realizing the universal principle force equals curvature:
Part I: The Euclidean Manifold as a Paradigm
Part II: Ariadne's Thread in Gauge Theory
Part III: Einstein's Theory of Special Relativity
Part IV: Ariadne's Thread in Cohomology
For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.
Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
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The author is a retired director of the Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany). He is a member of the German National Academy of Sciences, Leopoldina.Review:
From the reviews:
“This book is the third volume of a complete exposition of the important mathematical methods used in modern quantum field theory. It presents the very basic formalism, important results, and the most recent advances emphasizing the applications to gauge theory. ... the book’s greatest strength is Zeidler’s zeal to help students understand fundamental mathematics better. I thus find the book extremely useful since it signifies the role of mathematics for the road to reality ... .” (Gert Roepstorff, Zentralblatt MATH, Vol. 1228, 2012)
“The present book is a good companion to the literature on the subject of the volume title, especially for those already familiar with it. ... the book touches upon a large number of subjects on the interface between mathematics and physics, providing a good overview of gauge theory in both fields. It contains lots of background material, many historical remarks, and an extensive bibliography that helps the interested reader to continue his or her more thorough studies elsewhere.” (Walter D. van Suijlekom, Mathematical Reviews, Issue 2012 m)
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