Lectures on theoretical particle physics
Outline syllabi for the theoretical particle physics postgraduate
lectures. This gives an idea what might be offered. Depending on
prior knowledge of students and availability of lecturers, further
details will be arranged directly between students and lecturers.
- TPPG01: Group theory
- Introduction to groups. Transformation groups and symmetries
- Matrix groups. Examples
- Lie groups and their Lie algebras
- Representations of groups
- The groups SU(2), SO(3) and their representations
- The group SU(3) and its representations
- Outlook: Classification of Lie groups, examples of higher rank
Lie groups in particle physics
- TPPG02: Quantum Electrodynamics
- Recap Dirac equation, Noether theorem, conserved currents
- From global to local symmetries; U(1) gauge interaction; Lagrangian of QED
- Derivation of scattering amplitudes in Perturbation Theory; Feynman Rules of QED
- Gauge fixing; the photon propagator
- Electron-muon scattering; trace-building and calculus
- Mandelstam variables; crossing symmetries
- Cross section and decay rates; phase space integrals
- Electron-electron scattering
- Compton scattering
- TPPG03: Electroweak Interactions
- Introduction to weak Interactions
- Non-conservation of parity in weak interactions; Neutrinos
- Beta-decay. Muon decay. Computation of scattering amplitudes
- Neutrino-quark scattering; Cabibbo angle; Kobayashi-Maskawa matrices; discovery of the charm Quarks
- Electroweak Interactions; weak hypercharge; Weinberg angle
- Spontaneous symmetry breaking; Higgs mechanism
- Standard Model; Yukawa couplings; Vector boson masses; Fermion massless
- Outlook: Beyond Standard Model; Grand Unified Theories (GUT); Neutrino Oscillations; Supersymmetry.
- TPPG04: Quantum Chromodynamics
- Introduction and brief historical review; Isospin symmetry; SU(3) flavour symmetry; hadron multiplets
- Quarks and gluons; SU(3) colour; local SU(3) supersymmetry
- Classical Lagrangian of QCD; QCD as a QFT; gauges
- The theta term of QCD
- Feynman rules; colour factors in SU(N); simple QCD processes
- TPPG05: Renormalization Theory
- TPPG06: Supersymmetry
- Fermi-Bose supersymmetry
- Majorana fermions and charge conjugation
- Wess-Zumino Model
- Spontaneous supersymmetry breaking
- Supersymmetric gauge Theories
- The Supersymmetric Standard model
- TPPG07: Introduction to Supersymmetry and Superstrings.
- Supersymmetric harmonic oscillators
- Supersymmetry in 2 dimensions, the RNS model as a two-dimensional supersymmetric field theory
- The RNS string
- Spinors and supersymmetry algebras in diverse dimensions
- Representation theory of supersymmetry algebras. Central extensions and BPS states
- Overview of supersymmetric theories in diverse dimensions. Supergravity theories in 10 and 11 dimensions
- Superstrings and their relation to supergravity theories
- TPPG08: Introduction to String Theory
- Classical relativistic particles
- Classical relativistic strings
- Quantization of Relativistic Strings, Analysis of Spectrum
- Compactification, non-abelian gauge symmetries, T-duality
- TPPG09: Introduction to Lattice QCD
- Introduction: relating a quark mass to a hadron
- Path Integral of Euclidean QCD and Monte-Carlo
- Wilson formulation of the Gauge action and gauge invariance
- Fermions (1): Dirac operator on the lattice
- Fermions (2): Choosing the Lattice discretization, physics or politics?
- TPPG10: New strong dynamics beyond the standard model
- Composite Higgs paradigm
- Construction of representative composite Higgs models
- Partial compositeness for flavour physics
- UV completions of composite Higgs and partial compositeness
- Composite Higgs phenomenology: direct searches, electroweak precision observables, flavour physics
- Evidence for and characteristics of dark matter; composite paradigm
- Representative composite dark matter models and UV completions
- Composite dark matter phenomenology: direct detection, collider searches, gravitational waves
- Lattice field theory applications to composite Higgs and composite dark matter
- MAGIC081 - String Theory (Replacing TPPG08 since 2013 and delivered
through the MAGIC consortium)
- Relativistic particles
- Relativistic strings
- Conformal Field Theories: the massless scalar as example
- Conformal Field Theories: general aspects
- Space-time interpretation of string states
- Conformal Field Theories: Extended symmetries and Kac-Moody algebras (time permitting)
- Compactification of strings on a circle. T-duality (time permitting)
- Orbifolds (time permitting)
- TPPG11: Selected Topics in String Theory
- Surfaces (topology, G-structures) and string perturbation theory
- String path integral, ghosts, BRS symmetry
- World sheet CFT: fermions, bosonisation, BRS symmetry, bc-systems, picture changing, covariant superstring vertex operators
- World sheet CFT: from worldsheet to spacetime supersymmetry. Chiral rings and the worldsheet perspective on mirror symmetry
- Calabi-Yau manifolds and compactifications: Holonomy, Killing spinors and G-structures, moduli spaces, special geometry
