Quantum Field Theory. Pensumlist

[Home] Quantum Field Theory. Pensumlist

Introduction (Mulders, ch.1)
1. The subject of QFT -- elementary particles and their interactions.
2. Wave-particle duality. Fields and particles.
3. Units and notations.
Classical Lagrangian Field Theory (Mulders, ch.6.1)
1. Action. Lagrangian. Variational Principle. Euler-Lagrange equation.
2. Translation invariance. Energy-momentum tensor. Hamiltonian.
3. Gauge invariance. Conserved current.
Canonical quantization of a free scalar field (Mulders, ch.7.2)
1. Langrangian. Klein-Gordon equation. Normal modes.
2. Hamiltonian and Charge.
3. Quantization. Generation and anihilation operators. Commutation relations.
Transformational Properties of Fields (Mulders, ch.3)
1. Relativity principle and the group of coordinate transformations. The group of Lorentz transformations.
2. Lie groups and Lie algebras. Lie algebra of the Rotation Group. Lie algebra of the Lorentz Group.
3. 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.
4. Irreducible representations of the Lorentz group. Direct product of two irreducible representations.
5. Parity transformation. Bilinear forms of bispinors. Dirac matrices.
Quantization of Free Fields (Mulders, ch.6-7)
1. Real and complex scalar fields. Klein-Gordon equation. Plane-wave (normal mode) solutions. Generation and anihilation operators. Hamiltonian. Commutation relations.
2. Spin ½ field. Dirac equation. Plane-wave (normal mode) solutions. Generation and anihilation operators. Hamiltonian. Anticommutation relations.
3. Massive spin 1 field. Additional (Lorentz) condition to eliminate spin-0. Massless spin 1 field. Gauge invariance. Quantization within Coulomb (radiation) gauge.
4. Spin-statistics theorem. Discrete symmetries (C,P,T) (Mulders, ch.8). CPT theorem.
Interacting Quantum Fields (Mulders, ch.10)
1. Interaction Lagrangians and coupling constans. Interaction representation for the time evolution of the state vector. S-matrix. Cross sections.
2. Covariant perturbation theory. T-product and N-product of the field operators. Propagators. Wick's theorem.
3. Interaction of fermions and bosons, L_int=-gψψ(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)
1. Local gauge symmetry. Gauge theories. Non-Abelian gauge theories.
2. Spontaneous symmetry breaking. Goldstone theorem. Higgs mechanism.