Jeg har præciseret formuleringen af opgaven med et ekstra fire-divergens led i Lagrangianen på seddel~2.
Schedule:
Weekly notes:
Introduction.
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Exercises:
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The subject of quantum field theory: particles/fields.
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.
Mindste virknings princip ("blandt alle mulige bevægelser
vælger systemet den, som fører til målet med mindst
virkning."). Euler-Lagrange bevægelsesligning. Translationsinvarians
og energi-impuls bevarelseslov. Global qaugeinvarians og
kontinuitetsligning (bevarede strømme). Ladningsbevarelse. Noether sætning.
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 (Energi og ladning af feltet
i egensvingningstilstandsrepresentationen). 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.