Quantum Field Theory

The only graduate-level textbook on quantum field theory that fully integrates perspectives from high-energy, condensed-matter, and statistical physics

Quantum field theory was originally developed to describe quantum electrodynamics and other fundamental problems in high-energy physics, but today has become an invaluable conceptual and mathematical framework for addressing problems across physics, including in condensed-matter and statistical physics. With this expansion of applications has come a new and deeper understanding of quantum field theory―yet this perspective is still rarely reflected in teaching and textbooks on the subject. Developed from a year-long graduate course Eduardo Fradkin has taught for years to students of high-energy, condensed-matter, and statistical physics, this comprehensive textbook provides a fully “multicultural” approach to quantum field theory, covering the full breadth of its applications in one volume.

• Brings together perspectives from high-energy, condensed-matter, and statistical physics in both the main text and exercises
• Takes students from basic techniques to the frontiers of physics
• Pays special attention to the relation between measurements and propagators and the computation of cross sections and response functions
• Focuses on renormalization and the renormalization group, with an emphasis on fixed points, scale invariance, and their role in quantum field theory and phase transitions
• Other topics include non-perturbative phenomena, anomalies, and conformal invariance
• Features numerous examples and extensive problem sets
• Also serves as an invaluable resource for researchers

Table of Contents

1. Introduction to Field Theory

2. Classical Field Theory

3. Classical Symmetries and Conservation Laws

4. Canonical Quantization

5. Path Integrals in Quantum Mechanics and Quantum Field Theory

6. Nonrelativistic Field Theory

7. Quantization of the Free Dirac Field

8. Coherent-State Path-Integral Quantization of Quantum Field Theory

9. Quantization of Gauge Fields

10. Observables and Propagators

11. Perturbation Theory and Feynman Diagrams

12. Vertex Functions, the Effective Potential, and Symmetry Breaking

13. Perturbation Theory, Regularization, and Renormalization

14. Quantum Field Theory and Statistical Mechanics

15. The Renormalization Group

16. The Perturbative Renormalization Group

17. The 1/N Expansions

18. Phases of Gauge Theories

19. lnstantons and Solitons

20. Anomalies in Quantum Field Theory

21. Conformal Field Theory

22. Topological Field Theory

Review

“A very modern presentation of quantum field theory integrating applications to condensed-matter and high-energy particle physics. Fradkin’s approach both clarifies conceptual issues, such as the renormalization procedure, and presents many contacts with experiments.”―Juan Maldacena, Institute for Advanced Study in Princeton

“This superb textbook combines mathematical accuracy with keen physical intuition and a style that is precise yet friendly and easy to read. With his deep grasp of both condensed-matter physics and elementary-particle physics, Fradkin presents quantum field theory as a versatile and multifaceted tool to explore a wide range of physical phenomena.”―Natan Andrei, Rutgers University

“Fradkin connects the areas of high-energy and condensed-matter physics through the common language of quantum field theory. I do not know of another introductory text that does this so well.”―Frank Petriello, Northwestern University

“Fradkin has a deep understanding of a broad range of issues in quantum field theory, and he moves smoothly between particle physics and viewpoints in condensed matter and statistical mechanics. This exceptional book will be of great value to the theoretical physics community.”―Michael Dine, author of Supersymmetry and String Theory: Beyond the Standard Model

About the Author

Eduardo Fradkin is the Donald Biggar Willett Professor of Physics at the University of Illinois, Urbana-Champaign. An internationally recognized leader in theoretical physics and a member of the National Academy of Sciences, he is the author of Field Theories of Condensed Matter Physics.