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Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a reference for active researchers in the field.
1: Introduction
2: Relativistic Invariance
3: The Electromagnetic Field
4: General relativity: A Field Theory of Gravitation
5: The Physical States
6: Relativistic Wave Equations
7: Towards a Relativistic Quantum Mechanics
8: Functional Integrals and Probabilistic Amplitudes
9: Functional Integrals and Quantum Mechanics: Formal Developments
10: The Euclidean Functional Integrals
11: Fermions and Functional Formalism
12: Relativistic Quantum Fields
13: Applications
14: Geometry and Quantum Dynamics
15: Broken Symmetries
16: Quantum Field Theory at Higher Orders
17: A First Glance at Renormalisation and Symmetry
18: Renormalisation of Yang-Mills Theory and BRST Symmetry
19: Some Consequences of the Renormalisation Group
20: Analyticity Properties of Feynman Diagrams
21: Infrared Singularities
22: Coherent States and Classical Limit of Quantum Electrodynamics
23: Quantum Field Theories with a Large Number of Fields
24: The Existence of Field Theories beyond the Perturbation Expansion
25: Fundamental Interactions
26: Beyond the Standard Model
27: Supersymmetry, or the Defense of Scalars
Appendix A: Tensor Calculus
Appendix B: Differential Calculus
Appendix C: Groups and Lie Algebras
Appendix D: A collection of Useful Formulae
Appendix E: Extract from Maxwell's A Treatise on Electricity and Magnetism
Description
Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a reference for active researchers in the field.
