"Version: 20221201"--Title page verso.

Includes bibliographical references.

1. Gauge theories -- 1.1. Introduction to quantum electrodynamics -- 1.2. Abelian gauge invariance -- 1.3. Perturbative calculations at tree level in QED -- 1.4. Renormalization of QED -- 1.5. Compact Lie groups -- 1.6. Non-Abelian gauge theories -- 1.7. The Faddeev-Popov ansatz and gauge fixing for non-Abelian gauge theories -- 1.8. The geometry of gauge fields -- 1.9. Gauge fields compared to gravity -- 1.10. The Feynman rules for non-Abelian gauge theories -- 1.11. The Higgs mechanism

2. The renormalization group -- 2.1. Introduction -- 2.2. The Ising model -- 2.3. The order parameter and Landau theory -- 2.4. Critical exponents -- 2.5. The real-space renormalization group -- 2.6. Euclidean field theory -- 2.7. Derivation of the renormalization group equations : [phi]4 -- 2.8. The Wilson-Fisher fixed point -- 2.9. The effective action -- 2.10. Background field method for scalar field theories -- 2.11. The background field method for gauge theories -- Appendix. Simulation and the Metropolis algorithm

3. The 1/N expansion -- 3.1. Introduction -- 3.2. Quantum mechanics -- 3.3. Vector models in quantum mechanics -- 3.4. Vector models in quantum field theory -- 3.5. Matrix models in the large-N limit

4. Solitons and instantons -- 4.1. Introduction -- 4.2. The [phi]4 kink in 1 + 1 dimensions -- 4.3. Flux tubes -- 4.4. Magnetic monopoles -- 4.5. Instantons -- 4.6. False vacuum decay

5. Anomalies -- 5.1. Introduction -- 5.2. Path integral treatment of anomalies -- 5.3. Anomaly cancellation in gauge theories -- 5.4. The [eta][prime] problem and the U(1)A anomaly in QCD

6. Field theory at nonzero temperature -- 6.1. Introduction -- 6.2. Partition functions and path integrals -- 6.3. Free fields and Matsubara frequencies -- 6.4. Evaluation of the T [not equal to] 0 scalar field effective potential -- 6.5. Symmetry restoration -- 6.6. Running couplings -- 6.7. Fermions -- 6.8. Equilibration in field theories.

Quantum field theory is the theory of many-particle quantum systems. Just as quantum mechanics describes a single particle as both a particle and a wave, quantum field theory describes many-particle systems in terms of both particles and fields.

Graduate students studying particle physics, condensed matter.

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Professor Michael C. Ogilvie is a member of the physics department at Washington University. Prior to his appointment at the university, he held postdoctoral appointments at Brookhaven National Laboratory and the University of Maryland. He received his PhD from Brown University. His research interests include lattice gauge theory, extreme QCD and the theory of phase transitions.

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