Curriculum

Perimeter Scholars International is a 10 month intensive course, running from August to June each year. Graduates receive a Masters Degree in Physics from the University of Waterloo and a Perimeter Scholars International Certificate from Perimeter Institute for Theoretical Physics. All courses take place at Perimeter Institute for Theoretical Physics.

The course work is divided into four phases and is followed by a short research project, the Essay:

• Research Skills: problem formulation and solving and basic tools, including computers (2 weeks, full time).
• Core Topics: foundational subjects, such as quantum mechanics, relativity, field theory, statistical physics, dynamical systems, data analysis, and computation. (Four 3-week sessions, each with 2 courses running in parallel).
• Reviews: subdisciplinary subjects, such as particle physics, cosmology, and condensed matter physics. Students will choose from a selection of courses (Three 3-week sessions, each with 3 courses running in parallel. Students take 2 out of 3).
• Explorations: short, in-depth courses on specialized fields which are currently "hot." Students will choose from a selection of courses (Three 3-week sessions, each with 3 courses running in parallel. Students take 2 out of 3).
• Essay: Each student undertakes a short research project supervised by a local faculty member, and produces an essay which is publicly presented and defended.

The program also includes remedial English courses, training in scientific writing and presentation workshops. 

Although all course grades are either Credit or No Credit, PSI's approach to evaluation involves continuous assessment throughout the year conducted by PSI's resident tutors and Faculty. The goal is to encourage all students to achieve their potential and to avoid grade-chasing competition. The final grade on the PSI Certificate will be Distinction, Pass or Fail.

Core Courses

(3 weeks, 18 hours of lecture, 18 hours of tutorial)

1. PSI Quantum Field Theory 1 (Phys 601)
   Canonical quantization of fields, perturbation theory, derivation of Feynman diagrams, applications in particle and condensed matter theory, renormalization in φ⁴.
2. PSI Statistical Physics (Phys 602)
   A brief review of ensembles and quantum gases, Ising model, Landau theory of phase transitions, order parameters, topology, classical solutions.
3. PSI Quantum Field Theory 2 (Phys 603)
   Feynman Path Integral, abelian and nonabelian gauge theories and their quantization, spontaneous symmetry breaking, nonperturbative techniques: lattice field theory, Wilsonian renormalization.
4. PSI Relativity (Phys 604)
   Special relativity, foundations of general relativity, Riemannian geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties.
5. PSI Quantum Theory (Phys 605)
   Schrodinger equation: free particle, harmonic oscillator, simple time dependent problems. Heisenberg picture and connection with classical physics. Entanglement and non-locality. Pure and mixed states, quantum correlators, measurement theory and interpretation.
6. PSI Information and Data Analysis (Phys 606)
   Probability, entropy, Bayesian inference and Information theory. Maximum likelihood methods, common probability distributions, applications to real data including Monte Carlo methods.
7. PSI Dynamical Systems (Phys 607)
   Maps, flows, stability, fixed points, attractors, chaos, bifurcations, ergodicity, approach to chaos. Hamiltonian systems, Liouville measure, Poincare theorem, integrable systems with examples.
8. PSI Computation (Phys 608)
   Common algorithms for ode and pde solving, with numerical analysis. Common tasks in linear algebra. Focus on how to write good code, test it, and obtain a reliable result. Parallel programming.

Review Courses

6 of 9 (3 weeks, 18 hours of lecture, 18 hours of tutorial)

1. PSI Cosmology (Phys 621)
   FRW metric, Hubble expansion, dark energy, dark matter, CMB. Thermodynamic history of the early universe. Growth of perturbations, CDM model of structure formation and comparison to observations, cosmic microwave background anisotropies, inflation and observational tests.
2. PSI Standard Model (Phys 622)
   Application of Yang Mills theory to particle physics, QCD and its tests in the perturbative regime, theory of weak interactions, precision tests of electroweak theory, CKM matrix and flavour physics, open questions.
3. PSI String Theory (Phys 623)
   Superstring spectrum in 10d Minkowski, as well as simple toroidal and orbifold compactifications. T-duality, D-branes, tree amplitudes. Construct some simple unified models of particle physics. Motivate the 10- and 11-dimensional supergravities. Simple supergravity solutions and use these to explore some aspects of AdS/CFT duality.
4. PSI Mathematical Physics Topics (Phys 624)
   Differential forms, de Rham cohomology, differential topology and characteristic classes, monopoles and instantons, Kahler manifolds, Dirac equation, zero modes and index theorems.
5. PSI Quantum Information Review (Phys 635)
   Review of selected topics in Quantum Information.
6. PSI Gravitational Physics Review (Phys 636)
   Review of selected topics in Gravitational Physics.
7. PSI Condensed Matter Theory (Phys 637)
   Review of selected topics in Condensed Matter Theory.
8. PSI Quantum Gravity (Phys 638)
   Review of selected topics in Quantum Gravity.
9. PSI Foundations of Quantum Theory (Phys 639)
   Review of selected topics in Foundations of Quantum Theory.

Explorations Courses

6 of 9 (3 weeks, 18 hours of lecture, 18 hours of tutorial)

1. PSI Explorations in Quantum Information (Phys 641)
   Review of selected topics in Quantum Information.
2. PSI Explorations in Gravitational Physics (Phys 642)
   Review of selected topics in Gravitational Physics.
3. PSI Explorations in Condensed Matter Theory (Phys 643)
   Review of selected topics in Condensed Matter Theory.
4. PSI Explorations in Quantum Gravity (Phys 644)
   Review of selected topics in Quantum Gravity.
5. PSI Explorations in Foundations of Quantum Theory (Phys 645)
   Review of selected topics in Foundations of Quantum Theory.
6. PSI Explorations in Particle Physics (Phys 646)
   Review of selected topics in Particle Physics.
7. PSI Explorations in String Theory (Phys 647)
   Review of selected topics in String Theory.
8. PSI Explorations in Complex Systems (Phys 648)
   Review of selected topics in Complex Systems.
9. PSI Explorations in Cosmology (Phys 649)
   Review of selected topics in Cosmology.