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Quantum Field Theory. Pensumlist
- Classical Lagrangian Field Theory (Mulders, ch.6.1)
- Least Action Principle. Lagrangian. Euler-Lagrange equation.
- Energy-momentum tensor. Hamiltonian.
- Transformational Properties of Fields (Mulders, ch.3)
- Relativity principle and the group of coordinate
transformations. The group of Lorentz transformations.
- Lie groups and Lie algebras. Lie algebra of
the Rotation Group. Lie algebra of the Lorentz Group.
- Group Representations. Irreducible
representations of the rotation group. Direct product of two
irreducible representations. Reduction of
the direct product into a direct sum -- Clebsch-Gordan theorem.
- Irreducible representations of the Lorentz group. Direct
product of two irreducible representations.
- Parity transformation. Bilinear forms of bispinors. Dirac matrices.
- Quantization of Free Fields (Mulders, ch.6-7)
- Real and complex scalar fields. Klein-Gordon equation.
Plane-wave (normal mode) solutions. Generation and anihilation
operators. Hamiltonian. Commutation relations.
- Spin ½ field. Dirac equation. Plane-wave (normal mode)
solutions. Generation and anihilation
operators. Hamiltonian. Anticommutation relations.
- Massive spin 1 field. Additional (Lorentz) condition to
eliminate spin-0. Massless spin 1 field. Gauge invariance. Quantization
within Coulomb (radiation) gauge.
- Spin-statistics theorem. Discrete symmetries (C,P,T)
(Mulders, ch.8). CPT theorem.
- Interacting Quantum Fields (Mulders, ch.10)
- Interaction Lagrangians and coupling constans. Interaction
representation for the time evolution of the state vector. S-matrix. Cross
sections.
- Covariant perturbation theory. T-product and N-product
of the field operators. Propagators. Wick's theorem.
- Interaction of fermions and bosons,
Lint=-g
ψψ(φ+φ+). Feynman rules in
coordinate and momentum space. Scattering of
fermions. Non-relativistic limit. One boson exchange potential.
- Introduction to the Standard Model (Mulders, ch.12)
- Local gauge symmetry. Gauge theories. Non-Abelian gauge theories.
- Spontaneous symmetry breaking. Goldstone theorem. Higgs mechanism.
Copyleft © 2000-2002
D.V.Fedorov
(fedorov@ifa.au.dk)