Postgraduate Courses, Liverpool Theoretical Physics
Postgraduate Courses in Theoretical Physics (2020/2021)
Postgraduate lectures for first year postgraduate students:
 MATH425, Quantum Field Theory. Lecturer: Dr Martin Gorbahn.
Time and Place: 1st Semester, online, asynchronously (not timetabled).
Syllabus: see under current students on the departmental webpage .

MATH431, Introduction to Modern Particle Theory. Lecturer: Prof Alon Faraggi.
Time and Place: 2nd semester, online, asynchronously.
Syllabus: see under Current Students on the departmental webpage .

Additional lectures on theoretical particle physics. Outline syllabi:
see below.
Place and Time: tba.

MAGIC: The MAGIC consortium offers a range of online courses in mathematics
and mathematical physics for beginning PhD students. Liverpool PGR students
can register for any of these courses at the
MAGIC webpage.
Lectures are delivered synchronously (see MAGIC webpage for timetables)
via Zoom. Liverpool TP contributes MAGIC081, an introductory course in
string theory to the programme.
First year PhD students in Theoretical Physics should register
for MAGIC081 (participation and assessment) at the MAGIC webpage.
Schedule:
1st Semester 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Week (Oct 5  Oct 9)  
  12 noon MAGIC081  
Week (Oct 12  Oct 16)  
  12 noon MAGIC081  
Week (Oct 19  Oct 23)  
  12 noon MAGIC081  
Week (Oct 26  Oct 30)  
  12 noon MAGIC081  
Week (Nov 2  Nov 6)  
  12 noon MAGIC081  
Week (Nov 9  Nov 13)  
  12 noon MAGIC081  
Week (Nov 16  Nov 20)  
  12 noon MAGIC081  
Week (Nov 23  Nov 27)  
  12 noon MAGIC081  
Week (Nov 30  Dec 4)  
  12 noon MAGIC081  
Week (Dec 7  Dec 11)  
  12 noon MAGIC081  
Week Jan  
   
Week Jan  
   
2nd Semester 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Week 0  
   
Week 1  
   
Week 2  
   
Week 3  
   
Week 4  
   
Week 5  
   
Week 6  
   
Week 7  
   
Week 8  
   
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
 Electronmuon scattering; tracebuilding and calculus
 Mandelstam variables; crossing symmetries
 Cross section and decay rates; phase space integrals
 Electronelectron scattering
 Compton scattering

TPPG03: Electroweak Interactions.
 Introduction to weak interactions
 Nonconservation of parity in weak interactions; Neutrinos
 Betadecay. Muon decay. Computation of scattering amplitudes
 Neutrinoquark scattering; Cabibbo angle; KobayashiMaskawa matrices; discovery of the charm quark
 Electroweak Interactions; weak hypercharge; Weinberg angle
 Spontaneous symmetry breaking; Higgs mechanism
 Standard Model; Yukawa couplings; Vector boson masses; Fermion masses
 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) symmetry
 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.
 FermiBose symmetry
 Majorana fermions and charge conjugation
 WessZumino 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 twodimensional
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, nonabelian gauge symmetries, Tduality

TPPG09, Introduction to Lattice QCD.
 Introduction: relating a quark mass to a hardon
 Path Integral of Euclidean QCD and MonteCarlo
 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 charecteristics 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. Delivered
through the MAGIC consortium.
 Relativistic particles
 Relativistic strings
 Conformal Field Theories: the massless scalar as example
 Conformal Field Theories: general aspects
 Spacetime interpretation of string states
 Conformal Field Theories: Extended symmetries and KacMoody algebras
(time permitting)
 Compactification of strings on a circle. Tduality (time permitting)
 Orbifolds (time permitting)
Contact for this webpage:
Thomas Mohaupt.