(Wed. Dec. 7th) There will be lecture today all right.
There will be no lecture today, December 5th, sorry for that. There
will we an additional announcement about the Wednesday lecture.
You have to do three exercises from each chapter and send them to me either via email (with the
subject QFT16) or snailmail. The deadline for a given exercise is the Monday a week after the exercise.
We shall have exercises on Mondays 08:15 and lectures on Mondays 12:15 and Wednesdays 12:15.
Schedule:
Weekly notes:
Introduction.
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Exercises:
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The subject of quantum field theory.
Principle of Relativity.
Principle of covariance. Special theory of relativity. Four-vectors.
Classical Lagrangian field theory.
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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.
Canonical quantization of a free complex scalar field.
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Klein-Gordon equation. Normal modes (egensvingninger). Energy and
charge in normal mode representation
Number-of-particles
operators. Generation/annihilation operators. Statistics.
Transformational properties of fields.
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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.
Irreducible representations of the Lorentz group.
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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.
Spin-1/2 field.
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Bispinors. Bilinear forms of bispinors. Gamma-matrices.
Lagrangian. Dirac equation.
Canonical quantization of spin-1/2 field.
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Normal modes (plane-waves).
Charge and energy in normal mode representation. Generation-annihilation
operators: anti-commutation relation.
Spin-1 fields.
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Massive spin-1 field, Lorenz condition; Electromagnetic field, gauge
invariance, quantization in radiation gauge; Spin-statistics theorem.
Interacting quantum fields.
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Interaction Lagrangian; Time development
in quantum mechanics: Heisenberg,
Schrödinger, and interaction picture; S-matrix; Time-ordered product of
operators.
Feynman diagrams.
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Calculation of the S-matrix elements: time- and normal-products of field
operators; propagators; Wick's theorem; Feynman diagrams in coordinate space.
Higgs mechanism.
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Spontaneous symmetry breaking; The Higgs mechanism; The Standard Model.
Non-relativistic limit of QFT.
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Lippmann-Schwinger equation; One boson
exchange potential.
