QUANTUM FIELD THEORY
Professor John W. Norbury
Physics Department
University of Wisconsin-Milwaukee
P.O. Box 413
Milwaukee, WI 53201
November 20, 2000
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Contents
1 Lagrangian Field Theory
1.1 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Natural Units . . . . . . . . . . . . . . . . . . . . .
1.1.2 Geometrical Units . . . . . . . . . . . . . . . . . .
1.2 Covariant and Contravariant vectors . . . . . . . . . . . .
1.3 Classical point particle mechanics . . . . . . . . . . . . . .
1.3.1 Euler-Lagrange equation . . . . . . . . . . . . . . .
1.3.2 Hamilton’s equations . . . . . . . . . . . . . . . . .
1.4 Classical Field Theory . . . . . . . . . . . . . . . . . . . .
1.5 Noether’s Theorem . . . . . . . . . . . . . . . . . . . . . .
1.6 Spacetime Symmetries . . . . . . . . . . . . . . . . . . . .
1.6.1 Invariance under Translation . . . . . . . . . . . .
1.6.2 Angular Momentum and Lorentz Transformations
1.7 Internal Symmetries . . . . . . . . . . . . . . . . . . . . .
1.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8.1 Covariant and contravariant vectors . . . . . . . .
1.8.2 Classical point particle mechanics . . . . . . . . . .
1.8.3 Classical field theory . . . . . . . . . . . . . . . . .
1.8.4 Noether’s theorem . . . . . . . . . . . . . . . . . .
1.9 References and Notes . . . . . . . . . . . . . . . . . . . . .
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2 Symmetries & Group theory
2.1 Elements of Group Theory . . . . . . . . . .
2.2 SO(2) . . . . . . . . . . . . . . . . . . . . .
2.2.1 Transformation Properties of Fields
2.3 Representations of SO(2) and U(1) . . . . .
2.4 Representations of SO(3) and SU(1) . . . .
2.5 Representations of SO(N) . . . . . . . . . .
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