Quantum Field Theory
Dietrich Bödeker
Lecture notes, problem sheets
Why Quantum Field Theory?
1 Classical field theory, symmetries 1.1 Principle of least action 1.2 Lorentz invariance
Sheet 1
1.3 Hamiltonian formulation, 1.4 Noether's theorem
1.5 Complex Klein-Gordon field, 1.6 Poisson brackets, symmetry generators
Sheet 2
2 Scalar field quantization 2.1 Canonical quantization 2.2 Quantized real scalar field
2.3 Particles, spin, statistics 2.4 Complex scalar field
Sheet 3
2.5 Finite symmetry transformations
3 Correlation functions, interactions and scattering 2.1 Two-point functions, 2.2 Interactions
2.3 Energy spectrum, 2.4 Propagator
2.5 In and out states 2.6 Normalizable 1-particle states
Sheet 4
2.7 Lehmann-Symanzik-Zimmermann formula 2.8 Cross sections
3. Path integrals 3.1 Generating functional for n-point functions 3.2 Path integrals 3.3 Path integral for the generating functional
Sheet 5
3.4 Generating functional for free fields 3.5 Interactions, perturbation theory
3.6 Normalization factor 3.7 Two-point function at order lambda
Sheet 6
3.8 Four-point function at order lambda 3.9 Feynman rules
4 Renormalization 4.1 Full propagator 4.2 Counting divergenes 4.3 Regularization
Sheet 7
4.4 Dimensional regularization, 4.5 Mass renormalization
4.6 Four point function 4.7 Coupling constant renormalization
Sheet 8
4.8 Minimal subtraction 4.9 Renormalization group
4.10 Asymptotic behavior
Supplement: Lie algebras
5. Spin 1/2 fields and particles 5.1 Spinors
Sheet 9
5.3 Scalars and vectors built from spinors 5.4 Free Dirac equation
Sheet 10
5.5 Quantization, spin and statistics 5.6 Path integrals for fermions
5.7 Path integral for Dirac field, LSZ for Dirac fermions 6 Gauge fields 6.1 Canonical formulation
6.2 Path integral 6.4 Feynman propagator
Sheet 11
7 Quantum elelectrodynamics 7.1 Gauge invariance 7.2 Perturbation theory
Sheet 12
7.3 mu+ mu- pair creation
Supplement: spin sums
Sheet 13
7.4 Non-relativistic limit
7.5 Higher orders: vertex corrections
7.6 Vertex corrections at order α
Mathematica notebook
feynCalcGuide
Sheet 14
7.7 The anomalous magnetic moment
Literature, (some online books accessible only in the Uni VPN, see also Semesterapparat in the library)
Srednicki,
Quantum Field Theory
Peskin, Schroeder,
An Introduction to Quantum Field Theory
Weinberg,
The Quantum Theory of Fields Vol. 1 Foundations
Sterman,
An Introduction to Quantum Field Theory
Zee,
Quantum Field Theory in a Nutshell
Brown,
Quantum field theory
Ryder,
Quantum Field Theory
Online lecture notes:
Notes from Sidney Coleman's Physics 253a
Lecture notes by David Tong
, Cambridge
Specific topics:
Handouts by David B. Kaplan
Kaplan, Fermionic path intetgration
Path integrals in Quantum mechanics:
G. Münster,
Quantentheorie
Sakurai,
Modern quantum mechanics
Advanced topics in QFT:
Collins,
Renormalization
Collins,
A new approach to the LSZ reduction formula
Related topics:
Nachtmann,
Phänomene und Konzepte der Elementarteilchenphysik
Sexl, Urbantke,
Relativität, Gruppen, Teilchen
Gauge theory:
Lecture by M.Hairer