Course

This course will cover the mathematical structure underlying classical gauge theory. Previous knowledge of differential geometry is not required. Topics covered in the course include: introduction to manifolds, symplectic manifolds, introduction to Lie groups and Lie algebras; deformation quantisation and geometric quantisation; the matematical structure of field theories; scalar field theory; geometric picture of Yang-Mills theory; symplectic reduction. If time permits, we may also look at the description of gauge theory in terms of principal bundles and the topological aspects of gauge theory.

The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way. These mathematical tools will include a review of differential geometry (tensors, forms, Lie derivative), vielbeins and Cartan’s formalism, hypersurfaces, Gauss-Codazzi formalism, and variational principles (Einstein-Hilbert action & Gibbons-Hawking term). Several topics in black hole physics including the Kerr solution, black hole astrophysics, higher-dimensional black holes, black hole thermodynamics, Euclidean action, and Hawking radiation will be covered. Additional advanced topics will include domain walls, brane world scenarios, Kaluza-Klein theory and KK black holes, Gregory-Laflamme instability, and gravitational instantons

This course teaches basic numerical methods that are widely used across many fields of physics. The course is based on the Julia programming language. Topics include an introduction to Julia, linear algebra, Monte Carlo methods, differential equations, and are based on applications by researchers at Perimeter. The course will also teach principles of software engineering ensuring reproducible results.

Topics will include: Non-abelian gauge theory (aka Yang-Mills theory), the Standard Model (SM) as a particular non-abelian gauge theory (its gauge symmetry, particle content, and Lagrangian, Yukawa couplings, CKM matrix, 3 generations), spontaneous symmetry breaking: global vs local symmetries (Goldstone's Theorem vs Higgs Mechanism; mass generation for bosons and fermions), neutrino sector (including right-handed neutrinos?), effective field theory, Feynman rules (Standard Model propagators and vertices), gauge and global anomalies, strong CP problem, renormalization group (beta functions, asymptotic freedom, quark confinement, mesons, baryons, Higgs instability, hierarchy problem), unexplained puzzles in the SM, and surprising/intriguing aspects of SM structure that hint at a deeper picture.

The course has three parts. In the first part of the course, the path integral formulation of non-relativistic quantum mechanics and the functional integral formulation of quantum field theory are developed. The second part of the course covers renormalization and the renormalization group. Finally, non-abelian gauge theories are quantized using functional integral techniques.

The course begins by discussing several topics in equilibrium statistical physics including phase transitions and the renormalization group. The second part of the course covers non-equilibrium statistical physics including kinetics of aggregation, spin dynamics, population dynamics, and complex networks.

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

This is an introductory course on general relativity (GR). We shall cover the basics of differential geometry and its applications to Einstein’s theory of gravity. The plan is to discuss black holes, gravitational waves, and observational evidence for GR, as well as to cover some of the more advanced topics.

The course starts by looking for a quantum theory that is compatible with special relativity, without assuming fields are fundamental. Nevertheless fields turn out to be a very good, maybe inevitable mathematical tool for formulating and studying such a relativistic quantum theory. The second part of the course introduces the Dirac theory and canonically quantizes it. It also quantizes the Maxwell field theory. The Feynman diagram technique for perturbation theory is developed and applied to the scattering of relativistic fermions and photons. Renormalization of quantum electrodynamics is done to one-loop order.

Prerequisite: PSI Quantum Theory course or equivalently Graduate level Quantum Mechanics and QFT of scalar theory

This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity and classical field theory, with the emphasis on geometrical notions and relativistic formalism.

This course on quantum mechanics is divided in two parts:
 
The aim of the first part is to review the basis of quantum mechanics. The course aims to provide an overview of the perturbation theory to handle perturbations in quantum systems. Time evolution of quantum systems using the Schrodinger, Heisenberg and interaction pictures will be covered. Basics of quantum statistical mechanics for distinguishable particles, bosons, and fermions will be covered. A brief overview of density matrix approach and quantum systems interacting with the environment will be given.
 
The second part of the course is an introduction to scalar quantum field theory. The Feynman diagram technique for perturbation theory is developed and applied to the scattering of relativistic particles. Renormalization is briefly discussed.

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.