# PSI courses

The Perimeter Scholars International program starts in September and runs for 10 months to June of the following calendar year. Successful graduates of PSI will receive both a master's degree in physics from the University of Waterloo and a Perimeter Scholars International Certificate from the Perimeter Institute for Theoretical Physics. All courses take place at Perimeter Institute.

### Curriculum

The coursework is divided into two phases and a short research project in the form of an essay.

- Core Topics: foundational subjects, such as quantum mechanics, relativity, field theory, statistical physics, dynamical systems, data analysis, and scientific computation. (Three three- or four-week sessions, each with two courses running in parallel).
- Elective Courses: subdisciplinary subjects — such as particle physics, cosmology, quantum information, quantum foundations and condensed matter physics — and courses on specialized fields which are currently "hot." Students are required to take at least six.

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. Below is an example of a schedule from the year 2018/2019. It is subject to change each year to accommodate the needs of students.

### Assessment

Although all course grades are either "credit" or "no credit," PSI's approach to evaluation involves assessment throughout the year conducted by academic staff. This assessment is in the form of oral interviews (for core courses), homework assignments, and tutorial participation. The goal is to encourage all students to achieve their potential and to avoid grade-chasing competition.

September to December. The core courses cover foundational graduate-level subjects, and each course is three weeks long. Students take all core courses.

**Classical Physics**

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

**Quantum Theory**

This course on quantum mechanics is divided in two parts:

The aim of the first part is to review the basis of quantum mechanics from a point of view emphasizing the role of unitary representations of Lie groups in the theory. We will cover the basics of Lie groups, Lie algebras, and representation theory. The framework for this first part will be Dirac's approach, that is the canonical quantization procedure.

The aim of the second part is to introduce Feynman’s approach which is the path integral formalism, and which will be extensively used in quantum field theory.

**Quantum Field Theory I**

This course canonically quantizes scalar field theory. The Feynman diagram technique for perturbation theory is developed and applied to the scattering of relativistic particles. Renormalization plays an important role in the development of perturbation theory beyond leading order.

**Relativity**

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.

**Quantum Field Theory II**

This 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.

**Statistical physics**

The aim of this course is to explore the main ideas of the statistical physics approach to critical phenomena. We’ll start with a review of statistical mechanics concepts. We will then shift our focus to phase transitions, using the ferromagnetic phase transition and the Ising model as our primary example, with particular emphasis on the renormalization group (RG) approach. In the last part of the course we will briefly explore quantum phase transitions with the quantum version of the Ising model, as well as explore different numerical algorithms to study quantum Hamiltonian systems.

January to April. Elective courses introduce students to modern topics and cover cutting-edge research topics from various specialized subfields. Students take at least six out of fifteen courses. Each course is three weeks long. Recent courses and topics include:

**Quantum Field Theory III**

Functional integral quantization, non-abelian gauge theory.

**Condensed Matter**

Spontaneous symmetry breaking of continuous symmetries, goldstone modes, nonlinear sigma model, 2+epsilon and large-N expansion, 2d melting, hexatic phase, quantum spin chains, bosonization, Luttinger liquid, Fermi liquid, Cooper instability, Shankar-Polchinski RG, BCS superconductivity.

**Quantum Foundations**

The problem with the "textbook interpretation" of quantum mechanics. Operationalism vs. realism. The quantum measurement problem and a classification of research programs in terms of their proposed solution to it. Formulating quantum theory as an operational theory: density operators, positive operator-valued measures, completely positive trace-preserving maps, purification, Naimark extension, Stinespring dilation. Operational axiomatizations of quantum theory. Hidden variable models and the distinction between psi-ontic and psi-epistemic models. Hidden variable models based on an epistemic restriction. Bell’s theorem and locality. The Kochen-Specker theorem and noncontextuality. The deBroglie-Bohm intrerpretation. Dynamical Collapse Theories. The Everett Interpretation.

**Quantum Information**

Formulating quantum theory as an operational theory, Reversible computation, Quantum gates, Complexity, Algorithms, Error correction, Cryptography and information theory.

**Cosmology**

FRW universe, Dark energy, Cosmic Microwave Background, Big Bang Nucleosynthesis, Dark Matter, LCDM cosmology, Inflation, Primordial perturbations and QFT in curved space background.

**Machine Learning**

Training techniques for supervised learning, Feedforward neural networks, Monte Carlo methods, Convolutional neural networks, Unsupervised learning for data visualization and clustering, Reinforcement learning, Generative modelling: Boltzmann machines, recurrent neural networks, flow-based models, variational autoencoders, generative adversarial networks.

**Quantum Fields and Strings**

Conformal field theory, anomalies, introduction to string theory.Standard ModelStructure of standard model Lagrangian, spontaneous symmetry breaking.

**Relativistic Quantum Information (RQI)**

What is RQI? Research topics in RQI. Measuring quantum fields; The measurement problem and relativity. What is a particle detector? The light-matter interaction form first principles. Unruh-DeWitt detectors; practical quantum information on QFTs. Relativity, covariance and quantum optics; A critical view on the single-mode and rotating wave approximations. Measuring vacuum fluctuations. Non-inertial particle detectors and qubits in curved spacetimes. The Unruh effect: Original derivation with quantum information perspective. Thermality. Gibbs vs KMS. When Gibbs is not enough: The KMS condition in QFT. Thermalization of accelerated particle detectors: The Unruh effect, modern derivation. Entanglement structure of a QFT. Introduction to entanglement harvesting from the vacuum. Quantum Energy Teleportation and violation of energy conditions.

**Chern-Simons**

Review of differential forms and a very brief discussion of cohomology. Review of gauge fields, gauge invariance, field strength, and Wilson lines. The Chern-Simons Lagrangian. Gauge invariance and quantization of the level. Wilson lines and their topological invariance. Knot invariants from Wilson lines. Jones polynomial, and the relation between Wilson lines and the Jones polynomial. The phase space and the Hilbert space on a Riemann surface. Braid group actions on the Hilbert space in the presence of Wilson lines, and the Knizhnik-Zamolodchikov equation.

**Quantum Gravity**

Canonical formulation of constrained systems, The Dirac program, First order formalism of gravity, Loop Quantum Gravity, Spinfoam models, Discussions with invited speakers on: Space and Time in Quantum Gravity, Loop Quantum Cosmology, Black Holes, Other approaches of Quantum Gravity, Numerical methods in Spinfoam models, Research at PI.

**PhD — Beyond the Standard Model**

Right-handed neutrinos, Grand unification theories, Exceptional Jordan algebra.

**PhD — Chern-Simons**

The WZW model and Dirichlet boundary conditions for Chern-Simons theory. A careful derivation of the KZ equations using the WZW model. Further advanced topics chosen from among the following: Boundary monopoles and the WZW character, the Verlinde formula and WZW conformal blocks, fusion and modular tensor categories and quantum groups, other chiral boundary conditions, analytically continued Chern-Simons and the geometric Langlands program.

**PhD — Relativistic Quantum Information**

Entanglement harvesting: a deeper look. Entanglement farming from a QFT. Relativity and quantum and classical communication: Communication with particle detectors. Relativity and quantum and classical communication: Applications and fundamental aspects in cosmology. The Anti-Unruh effect and the Unruh effect without thermality. The measurement problem revisited.