// Aarhus University / Physics / Subatomic Physics / Theory >
Introduction to Quantum Field Theory. Autumn 2010.
[ Old Home ]
N.B.
  1. The examination is scheduled for 19-October-2010, 9:00-12:00, at the address: Åbogade 36 (behind Kræftens Bekæmpelse). I will not be there, but you are allowed to call me at my office, 89423651, to clarify the formulations of the examination problems.
  2. A footnote is added at note10 reminding that the operators within the interaction lagrangian are assumed to be in the normal order.
  3. The running headers on the lecture notes are reformatted into a logical sequence: note1, note2, ..., note13.
  4. You can ask your last questions on October 18th, 10:15-12:00, aud. 520-516.
  5. The examination is scheduled for October 19th. If this date is is really inconvenient for somebody, send me a message, we should be able to arrange a reexamination at some later date.
  6. Correction: note 5: in the discussion of the direct product of representation the correct term for the sum of generators is Kronecker sum, not direct sum.
Schedule:
Lectures: Wednesday, 10:15, Aud. 1525-323; and Thursday, 11:15, Aud. 1525-323.
Seminars: Monday, 10:15, Aud. 1525-323.
Weekly notes:
  1. Introduction.
    [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    The subject of quantum field theory. Particles and fields. Principle of covariance. Special theory of relativity. Four-vector notation.
  2. Classical Lagrangian field theory.
    [ ps | pdf | page-1.png; page-2.png; page-3.png; ] (last edit: 25.06)
    Principle of least action. Euler-Lagrange equation of motion. Translation invariance and energy-momentum tensor. Energy and momentum conservation. Global gauge invariance and conserved current. Charge conservation. Noether's theorem.
  3. Canonical quantization of a complex scalar field.
    [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    Klein-Gordon equation. Normal modes. Energy and charge in normal mode representation. Number-of-particles operator. Generation/annihilation operators. Statistics.
  4. Transformational properties of fields.
    [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06) [Exercises: ps | pdf | page-1.png]
    The group of coordinate transformations. Group representations. Lie groups and Lie algebras. Lie algebras of the rotation group and the Lorentz group. Irreducible representations of the rotation group.
  5. Irreducible representations of the Lorentz group.
     [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06) [Exercises: ps | pdf | page-1.png]
    Direct product of two representations of a group. Reduction of a direct product of two representations of the rotation group and the Lorentz group. Parity transformation. Finite rotation matrix.
  6. Spin-1/2 field.
     [ ps | pdf | page-1.png; page-2.png; page-3.png; ] (last edit: 25.06)
    Bispinors. Bilinear forms of bispinors. Gamma-matrices. Lagrangian. Dirac equation.
  7. Canonical quantization of spin-1/2 field.
     [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    Normal modes (plane-waves). Charge and energy in normal mode representation. Generation-annihilation operators: anti-commutation relation.
  8. Spin-1 fields.
     [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    Massive spin-1 field, Lorenz condition; Electromagnetic field, gauge invariance, quantization in radiation gauge; Spin-statistics theorem.
  9. Interacting quantum fields.
     [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    Interaction Lagrangian; Time development in quantum mechanics: Heisenberg, Schrödinger, and interaction picture; S-matrix; Time-ordered product of operators.
  10. Feynman diagrams.
    [ ps | pdf | page-1.png; page-2.png; page-3.png; page-4.png; ] (last edit: 25.06)
    Calculation of the S-matrix elements: time- and normal-products of field operators; propagators; Wick's theorem; Feynman diagrams in coordinate space.
  11. CPT theorem. Gauge theories.
    [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    CPT symmetry. Gauge theories: QED; Yang-Mills (non-abelian) theories.
  12. Higgs mechanism.
    [ ps | pdf | page-1.png; page-2.png; page-3.png; ] (last edit: 25.06)
    Spontaneous symmetry breaking; The Higgs mechanism; The Standard Model.
  13. Non-relativistic limit of QFT.
    [ ps | pdf | page-1.png; page-2.png; ] (last edit: 25.06)
    Lippmann-Schwinger equation; One boson exchange potential.
Literature:
P.J. Mulders, Quantum Field Theory, lecture notes.
Links:
A free textbook on field theory by Warren Siegel
Wikipedia
Copyleft © 2000-3000 D.V.Fedorov (fedorov (at) phys (dot) au (dot) dk)