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The aim of this course is to explore the main ideas of the statistical physics approach to critical phenomena. We will discuss phase transitions, using the ferromagnetic phase transition and the Ising model as our primary example, with particular emphasis on the renormalisation group approach. Instructor: Emilie Huffman / Maite Dupuis Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

Pedro has selected 9 papers for this mini-course.

• Infrared Photons and Gravitons by Weinberg, 1965
• Determination of an Operator Algebra for the 2D Ising Model by Kadanoff and Ceva, 1971
• Confinement of Quarks by Wilson, 1974,
• Phenomenological Lagrangians by Weinberg, 1979,
• Gravitational Effects on and of Vacuum Decay by Coleman and De Luccia, 1980
• Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions by Amati, Ciafaloni and Veneziano, 1987
• Quantum Spin Chains and The Haldane Gap by Affleck, 1988
• The Large N Limit of SFTs and Supergravity by Maldacena, 1997
• Entanglement Entropy and Quantum Field Theory by Calabrese and Cardy, 2008

The format will be: A] Pedro will give a 1h30m lecture about one of these papers on a Monday or a Friday (the Monday or Friday right after B] unless there is a holiday) B] One week later, X students give a presentation of Y minutes about important recent papers that refer/are related to that paper. At the end of this lecture we give feedback about those presentations. What is X and what is Y depends on how many students volunteer to present. Of course, people who just want to attend without presenting are also most welcome!

The aim of the first part is to present a brief overview of selected topics in quantum theory. Schrodinger, Heisenberg and Interaction picture is discussed and applied to study time evolution. Density matrix and Feynman path integral are introduced. The second part of the course derives the Feynman rules for scalar quantum field theory and introduces renormalization. Instructor: Bindiya Arora / Dan Wohns Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

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, thus setting the stage for the forthcoming courses in Quantum Mechanics, and Quantum Field Theory in particular, as well as in General Relativity and Quantum Gravity. Instructor: Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

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.

The course centers on an in-depth study of the symmetry structure of General Relativity and how this is intimately related to its dynamics and to the challenges posed to its quantization. To achieve this understanding, we will introduce a host of concepts and techniques, broadly (and loosely) known under the name of “Covariant Phase Space Method”. This provides a different perspective on GR’s physics, a perspective in which phase space, rather than spacetime, is front and center. We will apply these ideas and techniques to discuss the so-called Problem of Time, Wald's approach to black hole entropy as a Noether charge, and the relationship between Dirac's Hypersurface Deformation Algebra and GR's symmetries and dynamics. We will also discuss the problem of detecting single gravitons as well as crucial analogies and differences between a quantum electromagnetic and gravitational field. Lecture notes specific for the course will be provided.

We will discuss mathematical aspects of classical and quantum field theory, including topics such as: symplectic manifolds and the phase space, symplectic reduction, geometric quantization, Chern-Simons theory, and others.

Machine learning has become a very valuable toolbox for scientists including physicists. In this course, we will learn the basics of machine learning with an emphasis on applications for many-body physics. At the end of this course, you will be equipped with the necessary and preliminary tools for starting your own machine learning projects.

Classical probability theory makes the (mostly, tacit) assumption that any two random experiments can be performed jointly.  This assumption seems to fail in quantum theory.  A rapidly growing literature seeks to understand QM by placing it in a much broader mathematical landscape of ``generalized probabilistic theories", or GPTs,  in which incompatible experiments are permitted.   Among other things, this effort has led to  (i) a better appreciation that many "characteristically quantum" phenomena (e.g., entanglement)  are in fact generic to non-classical probabilistic theories, (ii) a suite of reconstructions of (mostly, finite-dimensional) QM from small packages of assumptions of a probabilistic or operational nature, and (iii) a clearer view of the options available for generalizing QM.  This course will offer a survey of this literature,  starting from scratch and concluding with a discussion of recent developments. 

Mathematical prerequisites: finite-dimensional linear algebra, ideally including tensor products and duality, plus some exposure to category theory (though I will briefly review this material as needed).  

Scheduling note: There will be 5 lectures from March 12-26, then a gap of two weeks before the final 2 lectures held April 16 & 18.

This course will cover phenomenological studies and experimental searches for new physics beyond the Standard Model, including: naturalness, extra dimension, supersymmetry, grand unification, dark matter candidates (WIMPs and axions) and their detection.

This survey course introduces some advanced topics in quantum field theory and string theory. Topics may include anomalies, conformal field theory, and bosonic string theory and are subject to change depending on the topics covered in the TBD elective course.