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, presentation skills and necessary background in computer and mathematics (4 weeks, full time).
• Core Topics: foundational subjects, such as quantum mechanics, relativity, field theory, statistical physics, dynamical systems, data analysis, and scientific computation. (Four 3-week sessions, each with 2 courses running in parallel).
• Reviews: subdisciplinary subjects, such as particle physics, cosmology, quantum information, quantum foundations 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 or outside 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 Pass or Fail.

Core Courses

(3 weeks, 18 hours of lecture, 14 hours of tutorial)

1. PSI Quantum Theory
   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.
2. PSI Relativity
   Special relativity, foundations of general relativity, Riemannian geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties.
3. PSI Quantum Field Theory 1
   Canonical quantization of fields, perturbation theory, derivation of Feynman diagrams, applications in particle and condensed matter theory, renormalization in φ⁴.
4. PSI Statistical Mechanics
   A brief review of ensembles and quantum gases, Ising model, Landau theory of phase transitions, order parameters, topology, classical solutions.
5. PSI Quantum Field Theory 2
   Feynman Path Integral, abelian and nonabelian gauge theories and their quantization, spontaneous symmetry breaking, nonperturbative techniques: lattice field theory, Wilsonian renormalization.
6. PSI Condensed Matter
   The general principles guiding the course will be broken symmetries, phases and emergent collective modes.
7. PSI Mathematical Physics
   This course will include the study of Perturbation Theory (Regular and Singular) Speeding Up Convergence and the Gibbs Phenomenon.
8. PSI Conformal Field Theory
   An introduction to the key ideas and techniques of CFT. These theories play a central role in the study of phase transitions in statistical physics and condensed matter systems, as well as in string theory.

Review Courses

6 of 9 (3 weeks, 18 hours of lecture, 14 hours of tutorial)

1. PSI Standard Model
   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.
2. PSI Cosmology
   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.
3. PSI Quantum Foundations
   Operational and realistic approaches to the interpretation of quantm mechanics. Local realism and the EPR argument. Bell's theorem and non-locality. Contextuality and the Kochen-Specker theorem. The deBroglie-Bohm interpretation. The many world interpretation.
4. PSI Quantum Gravity
   Linear gravity and gravitons. Gravitational path integral. Pertubative Lorentzian quantum gravity (QG) and the need for non-pertubative QG. Constrained Hamiltonian systems. Canonical formulation of GR. Non-pertubative canonical QG. The Wheeler-De Witt equation. Loop QG. Non-perturbative path-integral for gravity: lattice and discrete methods (Regge calculus) and causal dynamical triangulations (CDT). Surprises in non-perturbative approach.
5. PSI Gravitational Physics Review
   Relativist's toolkit: the geometric framework of GR, Cartan formalism, Gauss-Codazzi equations and Kaluza Klein theories. Black Holes: 4D solutions, black hole theorems, Hawking radiation and thermodynamics. Extra dimensions: simple supergravity solutions in string theory (branes), the stability of these objects, then braneworlds and warped extra dimensions.
6. PSI Quantum Information Review
   Basic concepts: qubits, quantum gates, quantum circuits, density matrices, quantum operations, entropy, entanglement.  Topics in quantum algorithms and complexity: Languages, complexity classes, oracles, RSA, Deutsch-Jozsa algorithms, Shor's algorith, Grover's algorigthm.  Information theory and implementations: Overview of implementations, quantum error correction, quantum cryptography, quantum information theory.
7. PSI String Theory
   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
8. PSI Condensed Matter Theory
   This class will aproach the following topics: Properties of Normal Metals, Non-interacting Electrons, Interactions (Hartree-Fock Approach; Landau Fermi theory), Properties of Low-Temperature Superconductors, Pairing and Bardeen-Cooper-Schrieffer theory,  Phenomenological Description of Superconductivity, Properties of High-Temperature Superconductors, Models for Unconventional Superconductivity, Exterded Hubbard Model.
9. PSI Beyond the Standard Model
   Evidence and rationale for physics beyond the Standard Model: Neutrinos, Baryogenesis, dark matter, scale hierarchies, electro-weak precision experiments; BSM Physics: Supersymmetry (a tale of unification), Technicolor (superconductivity at the LHC), Extra-dimensions (Black holes, holography and strong coupling).

 

Explorations Courses

4 of 6 (3 weeks, 18 hours of lecture, 14 hours of tutorial)

1. PSI Explorations in Quantum Information
   Review of selected topics in Quantum Information.
2. PSI Explorations in Condensed Matter Theory
   Review of selected topics in Condensed Matter Theory.
3. PSI Explorations in String Theory
   Review of selected topics in String Theory.
4. PSI Explorations in Cosmology
   Review of selected topics in Cosmology.
5. PSI Explorations in Particle Theory
   Review of selected topics in Particle Theory.
6. PSI Explorations in Numerical Relativity
   Review of selected topics in Numerical Relativity.