“The public has a distorted view of science because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries.”
― Freeman J. Dyson
About this course:
- Lecturer: PD Dr. B. Kubis
- Year: 2017/2018
- Difficulty:
- Course page: eCampus
- Tutor: M. Niehus
- Literature:
The sequel to Quantum Field Theory, covering some advanced concepts that were not discussed in the first course. In part, the topics are pretty tough, but it was still a great course to get a deeper understanding of quantum field theory. The exercises were compulsory.
Exercise 1:
Keywords: Real Scalar Field, Six-dimensional, Metastable Vacuum State, Renormalization Scale μ, One-particle-irreducible Diagrams, One-loop Diagrams, Superficial Degree of Divergence, Minimal Subtraction Scheme, MS Scheme, Dimensional Regularization, Digamma Function, Euler-Mascheroni Constant, Counterterms
- Renormalization of ϕ³ Theory in six Dimensions
Exercise 2:
Keywords: Ground State to Ground State Transition, Transition Amplitude, Harmonic Oscillator, External Force, Path Integral Formalism, Propagator, Schrödinger Equation, Time-evolution Operator
- Harmonic Oscillator with External Force
- Time-evolution Operator and Schrödinger Equation
Exercise 3:
Keywords: Multi-dimensional Integrals, Gauss Integrals, Gaussian Integral, Grassmann Variables, Grassmann Algebra, Integration over Grassmann Variables, Differentiation on Grassmann Variables, ϕ⁴ Theory, Generating Functional, Propagators, Loops, External Currents, Four-point Function
- Gauss Integrals and Grassmann Variables
- Generating Functional and Two-point Function for ϕ⁴
Exercise 4:
Keywords: Generating Functional, Connected Green’s Functions, Functional Derivatives, Classical Field, Classical Action, Legendre Transform, Effective Action, Two-point Function, Three-point Function
- Effective Action and Legendre Transformations
Exercise 5:
Keywords: Fermion Vertex Function, Leading-order Correction, Invariant Matrix Element, Vertex Function, Ward Identity, Gordon Identity, Dirac Form Factor, Pauli Form Factor, Projection Operator, Loop Integrals, Magnetic Moment, Anomalous Magnetic Moment
- Fermion Magnetic Moment
Exercise 6:
Keywords: Loop Integrals, Feynman Parameter, Dimensional Regularization Integral, Digamma Function, Euler-Mascheroni Constant, Dispersion Relation, Discontinuity, Imaginary Part, Cauchy’s Integral Formula, Branch Cut, Unsubtracted Dispersion Relation, Subtracted Dispersion Relation
- Loop Integrals
Exercise 7:
Keywords: Infrared Divergences, Radiative Corrections, Virtual Corrections, Bremsstrahlung, Feynman Rules, Photon Mass Regulation, Wave Function Renormalization, Differential Decay Rate, Soft-photon Approximation, Energy Cutoff, Infrared Cancellation
- Infrared Divergences
Exercise 8:
Keywords: Heavy Scalar Field, Fermion Field, Path Integral Formalism, Generating Functional, Source Terms, Interaction Part, Effective Interaction Lagrangian, Non-local Operator, Heavy Field Feynman Propagator, Momentum Cutoff, Local Effective Lagrangian
- Integrating out a Heavy Field
Exercise 9:
Keywords: Equivalent to Renormalization Group Equations, One-dimensional Liquid, Bacterial Population, Bacteria Growth Rate, Partial Differential Equation, N-point Vertex Function, Differential Equation
- Classical Analogy to Renormalization Group Equations
- Differential Equation for N-point Function
Exercise 10:
Keywords: Running Coupling, Ultraviolet Behavior, β-function, Asymptotic Behavior, Differential Equation, Ultraviolet Stable Fixed Point, QCD Lagrangian, Quark Field, Gluon Field, Strong Coupling Constant, Structure Constants, Gell-Mann Matrices, Quark-Gluon Vertex, Triple-Gluon Vertex, Quadrupole-Gluon Vertex
- Behavior of ḡ near a Simple Fixed Point
- Running Coupling near a General Fixed Point
- Vertices in QCD
Exercise 11:
Keywords: Ghost Fields, Gauge Field Determinant, Unitarity, S-Matrix, One-loop Level, Optical Theorem, Fermion-Anti-fermion Scattering, SU(2) Gauge Theory, Massless Gauge Boson Intermediate States, Feynman Gauge, Polarization Sums
- Ghosts and Unitarity
Exercise 12:
Keywords: Quantum Electrodynamics, Renormalized Coupling, Bare Coupling, Vacuum Polarization, Dimensional Regularization, Running Coupling, β-function, Decoupling Behavior, Subtraction Schemes
- Running Coupling in QED
Exercise 13:
Keywords: Triangle Anomaly, VVA Triangle Anomaly, Divergent Loop Integrals, Shift of Integration Measure, AAA Triangle Anomaly, Isospin Group, Neutral Pion Decay, π⁰ Decay, π⁰ → γγ, Matrix Element, Pion Decay Constant, Decay Width
- The Triangle Anomaly
- Neutral Pion Decay