Quantization of Gauge Systems
eBook - PDF

Quantization of Gauge Systems

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Quantization of Gauge Systems

About this book

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail.


The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

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Yes, you can access Quantization of Gauge Systems by Marc Henneaux,Claudio Teitelboim in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover Page
  2. Half-title Page
  3. Title Page
  4. Copyright Page
  5. Contents
  6. Preface
  7. Acknowledgments
  8. Notations
  9. Chapter One: Constrained Hamiltonian Systems
  10. Chapter Two: Geometry of the Constraint Surface
  11. Chapter Three: Gauge Invariance of the Action
  12. Chapter Four: Generally Covariant Systems
  13. Chapter Five: First-Class Constraints: Further Developments
  14. Chapter Six: Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra
  15. Chapter Seven: Constrained Systems with Fermi Variables
  16. Chapter Eight: Graded Differential Algebras—Algebraic Structure of the BRST Symmetry
  17. Chapter Nine: BRST Construction in the Irreducible Case
  18. Chapter Ten: BRST Construction in the Reducible Case
  19. Chapter Eleven: Dynamics of the Ghosts—Gauge-Fixed Action
  20. Chapter Twelve: The BRST Transformation in Field Theory
  21. Chapter Thirteen: Quantum Mechanics of Constrained Systems: Standard Operator Methods
  22. Chapter Fourteen: BRST Operator Method—Quantum BRST Cohomology
  23. Chapter Fifteen: Path Integral for Unconstrained Systems
  24. Chapter Sixteen: Path Integral for Constrained Systems
  25. Chapter Seventeen: Antifleld Formalism: Classical Theory
  26. Chapter Eighteen: Antifield Formalism and Path Integral
  27. Chapter Nineteen: Free Maxwell Theory. Abelian Two-Form Gauge Field
  28. Chapter Twenty: Complementary Material
  29. Bibliography
  30. Index