Appendices

C - Trinity Courses

Advanced Topics in Plasma Physics

Department: Physics

Lecturer: Dr Daniel Kennedy 

Course Weight: 0.75 units/12 lectures 

Assessment Method: homework completion only

Course Synopsis: Basics of magnetic-confinement fusion. Magnetic geometry and flux surfaces in toroidal devices. Equilibrium vs fluctuations. Scale separation in time and space. 
Asymptotic expansion the Vlasov-Landau equation. Gyrokinetic variables and gyroaverages. Derivation of the gyrokinetic equilibrium. Equilibrium Maxwell’s equations. Derivation of the gyrokinetic equation for plasma fluctuations. Fluctuating Maxwell’s equations. Free-energy conservation in gyrokinetics.Plasma instabilities. Linear gyrokinetic theory and temperature-gradient-driven instabilities.

Astroparticle Physics

Department: Physics

Lecturer: Prof Joseph Conlon

Course Weight: 1 unit/16 lectures

Assessment Method: homework completion only

Pre-requisites: Quantum Field Theory (MT), General Relativity I (MT)

Course synopsis: The Universe observed, constructing world models, reconstructing our thermal history, decoupling of the cosmic microwave background, primordial nucleosynthesis. Dark matter: astrophysical phenomenology, relic particles, direct and indirect detection. Cosmic particle accelerators, cosmic ray propagation in the Galaxy. The energy frontier: ultrahigh energy cosmic rays and neutrinos. The early Universe: constraints on new physics, baryo/leptogenesis, inflation, the formation of large-scale structure, dark energy.

Collisional Plasma Physics

Department: Physics

Lecturer: Prof Alex Schekochihin

Course Weight: 1 unit/16 lectures

Assessment Method: homework completion only

Prerequisites: Kinetic Theory (MT), Advanced Fluid Dynamics (HT), Collisionless Plasma Physics (HT)

Course Synopsis: Collision operators: Fokker-Plank collision operator, conservation properties, entropy, electron-ion and ion-electron collisions, linearized collision operator. Collisional transport (Braginskii equations: derivation of Spitzer resistivity and electron heat conduction, ion heat conduction and viscosity. Resistive MHD: tearing modes, magnetic reconnection. Introduction to tokamak theory: Pfirsch-Schlueter collision transport regime for electrons.

Conformal Field Theory

Department: Maths

Lecturer: Prof Robin Karlsson

Course Weight: 1 unit/16 hours

Assessment Method: homework completion only 

Prerequisites: Quantum Field Theory (MT)

Course Synopsis: 
-    Motivation: RG flows and scale invariance.
-    Conformal transformations.
-    Consequence of conformal invariance.
-    Radial quantization and the operator algebra.
-    Conformal invariance in two dimensions.
-    The Virasoro algebra.
-    Minimal models.
-    Conformal bootstrap in d > 2.

Machine Learning Fundamentals with Applications to Physics and Mathematics

Department: Physics

Lecturer: Dr Andrei Constantin

Course Weight: 1 unit/16 lectures

Assessment Method: homework completion only 

Prerequisites: Prior exposure to Mathematica and Python will be helpful, but not mandatory.

Course Synopsis: Over the past five to ten years, machine learning and artificial intelligence in general, have evolved into indispensable research tools. This course seeks to offer a comprehensive introduction to the diverse array of machine learning techniques. These methods share the common goal of crafting algorithms that enable computers to make predictions and decisions autonomously, without relying on explicit, handcrafted rules. Using these techniques, one can extract valuable insights from computers that surpass the information initially provided. 
The course will discuss fundamental principles, algorithms, and a number of applications in Mathematics and Physics, including state reconstruction in quantum physics, model building in particle physics and cosmology, applications to string theory compactifications, conformal bootstrap and knot theory. 

Quantum Field Theory in Curved Space-Time

Department: Maths

Lecturer: Dr Pieter Bomans

Course Weight: 1 unit/16 lectures 

Assessment Method: homework completion only

Prerequisites: Quantum Field Theory (MT), General Relativity I (MT) and General Relativity II (HT). Advanced Quantum Field Theory and a course on differential geometry will be helpful but not essential.

Course Synopsis: This course builds on the courses in quantum field theory and general relativity. It will focus on classical and quantum aspects of fields in curved space-time. The course will consist of the following topics: Classical fields in curved space, Quantization in curved space, Quantum fields in (Anti) de Sitter space, Quantum fields in Rindler space and the Unruh effect, Hawking radiation, Black hole thermodynamics and the Hawking-Page phase transition, Interactions in curved space-time, Quantum field theory and cosmology.

Quantum Matter 4: Renormalization and Bosonization

Department: Physics

Lecturer: Prof Shivaji Sondhi

Course Weight: 1 unit/16 lectures 

Assessment Method: homework completion only

Prerequisites: Although the lectures will be self-contained, this course is designed as a follow-on to Quantum Matter II. Familiarity with ideas introduced in Advanced Quantum Theory and Renormalization Group will be useful but not essential.

Course synopsis: Modern condensed matter physics is increasingly focused on understanding the properties of strongly interacting systems. Traditional techniques that rely on diagrammatic perturbation theory about the independent electron approximation are often insufficient to provide an adequate description of the rich phenomena possible in this setting. Instead, their study requires a variety of ideas often also invoked in the study of quantum field theories in the non-perturbative regime. This course will cover two of these ideas: the renormalization group and (abelian) bosonization.

Renormalization group for Interacting Fermions: momentum-shell RG for φ4 theory; RG and the Fermi surface; BCS and CDW as competing instabilities; RG in d=1 and emergence of Luttinger liquids

Bosonization: Fermion-boson dictionary; application to spinless fermions; sine-Gordon model and Kosterlitz-Thouless flow; emergence of insulators from commensuration

Renormalisation Group

Department: Maths

Lecturer: Prof Fernando Alday

Course Weight: 1 unit/16 lectures 

Assessment Method: homework completion only

Prerequisites: Quantum Field Theory (MT), C5.3 Statistical Mechanics (HT) or equivalent

Course Synopsis: This course introduces ideas of scale-invariance and the renormalisation group in statistical physics, using simple lattice models and field theories as examples. Topics include: Real space RG; Fixed points, scaling operators, operator product expansion etc.; Landau Ginsburg theory; Mean field theory; Large N approximation; the 4-epsilon expansion; the 2+epsilon expansion; the Kosterlitz-Thouless transition; The Sine-Gordon model; XY duality.

String Theory II

Deaprtment: Maths

Lecturer: Prof Xenia de la Ossa

Course Weight: 1 unit/16 lectures

Assessment Method: homework completion only

General Prerequisites: Quantum Field Theory (MT), String Theory I (HT) , Advanced Quantum Field Theory (HT), Supersymmetry and Supergravity (HT)

Course Synopsis: Classical superstring action, RNS string, quantization and GSO-projection; 10d superstrings: Type IIA, IIB, I and Heterotic strings; Open strings and D-branes; Supergravities and spacetime effective actions, M-theory and 11d supergravity; Compactifications; Dualities between string theories.

The Standard Model and Beyond I

Department: Physics

Lecturer: TBC

Course Weight: 1 unit/ 16 lectures 

Assessment Method: homework completion only

Prerequisite: Advanced Quantum Field Theory (HT)

Course Synopsis: Basics of strong interactions: the peculiarities of asymptotic freedom and the uniqueness of gauge theories. Low-energy effective actions: from QCD to the chiral Lagrangian, and Effective Field Theories. Building the Electroweak sector of the Standard Model. Exploring the structure of the Electroweak sector. QCD at colliders [if time permits]: OPE and factorisation, from hadrons to partons
You may find the following textbooks useful: H. Georgi, Weak Interactions and Modern Particle Theory; J.F. Donoghue, E. Golowich, Barry R. Holstein, Dynamics of the standard model.

The Standard Model and Beyond II

Department: Physics

Lecturer: Prof John March-Russell

Course Weight: 1 unit/16 lectures 

Assessment Method: homework completion only 

Prerequisite: Advanced Quantum Field Theory (HT)

Topics in Soft and Activer Matter Physics

Department: Physics

Lecturer: Prof Ard Louis

Course Weight: 0.5 units/8 lectures

Assessment Method: homework completion only

Prerequisites: Advanced Fluid Dynamics (HT)

Course Synopsis: 
This is a reading course. Under the guidance of the course organiser, students will give presentations based on key papers in soft condensed matter theory. Some examples of the topics for these presentations are: Active nematics and active gels. Wetting, spreading and contact line dynamics. Hydrodynamics of microswimmers: Stokes equation, scallop theorem, multipole expansion, active suspensions. Fluctuations and response.