Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Relativistic Quantum Mechanics
- 2 Fock Space, the Scalar Field, and Canonical Quantization
- 3 Symmetries and Conservation Laws
- 4 From Dyson's Formula to Feynman Rules
- 5 Differential Transition Probabilities and Predictions
- 6 Representations of the Lorentz Group
- 7 Two-Component Spinor Fields
- 8 Four-Component Spinor Fields
- 9 Vector Fields and Gauge Invariance
- 10 Reformulating Scattering Theory
- 11 Functional Integral Quantization
- 12 Quantization of Gauge Theories
- 13 Anomalies and Vacua in Gauge Theories
- 14 SU(3) Representation Theory
- 15 The Structure of the Standard Model
- 16 Hadrons, Flavor Symmetry, and Nucleon-Pion Interactions
- 17 Tree-Level Applications of the Standard Model
- 18 Regularization and Renormalization
- 19 Renormalization of QED: Three Primitive Divergences
- 20 Renormalization and Preservation of Symmetries
- 21 The Renormalization Group Equations
- Appendix
- References
- Index
Preface
Published online by Cambridge University Press: 31 October 2009
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Relativistic Quantum Mechanics
- 2 Fock Space, the Scalar Field, and Canonical Quantization
- 3 Symmetries and Conservation Laws
- 4 From Dyson's Formula to Feynman Rules
- 5 Differential Transition Probabilities and Predictions
- 6 Representations of the Lorentz Group
- 7 Two-Component Spinor Fields
- 8 Four-Component Spinor Fields
- 9 Vector Fields and Gauge Invariance
- 10 Reformulating Scattering Theory
- 11 Functional Integral Quantization
- 12 Quantization of Gauge Theories
- 13 Anomalies and Vacua in Gauge Theories
- 14 SU(3) Representation Theory
- 15 The Structure of the Standard Model
- 16 Hadrons, Flavor Symmetry, and Nucleon-Pion Interactions
- 17 Tree-Level Applications of the Standard Model
- 18 Regularization and Renormalization
- 19 Renormalization of QED: Three Primitive Divergences
- 20 Renormalization and Preservation of Symmetries
- 21 The Renormalization Group Equations
- Appendix
- References
- Index
Summary
After completing my dissertation in differential geometry, I returned to Maharishi University of Management to join the faculty there. The greatest need for my services was in the physics department, and the chairman, the well-known John Hagelin, pointed the finger of authority and said ‘quantum field theory!’ The class was to start in a few weeks. I laughed, but John was serious.
Fortunately, I had audited Sidney Coleman's outstanding Harvard lectures and had taken very good notes. Equally fortunate, I had Robert Brandenburger's official solutions to all the homework sets. I rolled up my sleeves and waded in.
As we battled through the material, the beautiful architecture of Coleman's course became apparent. It introduced the primary concepts — canonical quantization, renormalization, spin, functional integral quantization — one at a time and made each one practical before advancing to the next abstraction. It started with simple models and provided motivation for each elaboration.
The students, however, pinned me to the board with questions about every step in the logic. Could I produce some mathematics to fill the gap? Was there a physical principle which would justify the proposed step? The standard references failed to meet the need, and for the most part I was stumped.
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- Chapter
- Information
- Quantum Field Theory for Mathematicians , pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 1999