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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.

This course will cover the basics of Quantum Foundations under three main headings. Part I – Novel effects in Quantum Theory. A number of interesting quantum effects will be considered. (a) Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, (b) The quantum-Zeno effect. (c) The no cloning theorem. (d) Quantum optics (single mode). Hong-Ou-Mandel dip. Part II Conceptual and interpretational issues. (a) Axioms for quantum theory for pure states. (b) Von-Neumann measurement model. * (c) The measurement (or reality) problem. (d) EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. (e) Bell’s theorem, nonlocality without inequalities. The Tirolson bound. (f) The Kochen-Specker theorem and related work by Spekkens (g) On the reality of the wavefunction: Epistemic versus ontic interpretations of the wavefunction and the Pusey-Barrett-Rudolph theorem proving the reality of the wave function. (h) Gleason’s theorem. (i) Interpretations. The landscape of interpretations of quantum theory (the Harrigen Spekkens classification). The de Broglie-Bohm interpretation, the many worlds interpretation, wave-function collapse models, the Copenhagen interpretation, and QBism. Part III Structural issues. (a) Reformulating quantum theory: I will look at some reformulations of quantum theory and consider the light they throw on the structure of quantum theory. These may include time symmetric quantum theory and weak measurements (Aharonov et al), quantum Bayesian networks, and the operator tensor formalism. (b) Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. (c) Reasonable principles for quantum theory: I will review some of the recent work on reconstructing quantum theory from simple principles. (d) Indefinite causal structure and indefinite causal order. Finally I will conclude by looking at (i) the close link between quantum foundations and quantum information and (ii) possible future directions in quantum gravity motivated by ideas from quantum foundations.

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.

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.

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

The goal of this Winter School on Symmetries is to introduce graduate students to the effectiveness of symmetry principles across subjects and energy scales. 

From Noether’s celebrated theorem to the development of the standard model of particle physics, from Landau’s to Wilson’s classification of phases of matter and phase transitions, symmetries have been key to 20th century physics. But in the last decades novel and more subtle incarnations of the symmetry principle have shown us the way to unlocking new and unexpected phases of quantum matter, infrared and holographic properties of the quantum gravitational interaction, as well as to advancements in pure mathematics to mention a few.  

The Graduate Winter School on Symmetries will introduce students and young researchers to a variety of applications of the symmetry principle. These will be chosen across contemporary research topics in both theoretical physics and mathematics. Our goal is to create a synergistic environment where ideas and techniques can ultimately spread across disciplines. This will be achieved through a combination of mini-courses, colloquia, and discussion sessions led in collaboration with the students themselves.

https://pirsa.org/C23008

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

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 workshop will bring together a group of young trendsetters working at the frontier of machine learning and quantum information. The workshop will feature two days of talks, and ample time for participants to interact and form new collaborations in the inspiring environment of the Perimeter Institute. Topics will include machine learning, quantum field theory, quantum information, and unifying theoretical concepts.

https://pirsa.org/C22034

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

The goal of this conference is for quantum matter researchers at Perimeter, University of British Columbia, and University of Toronto to share their recent work with each other, to facilitate discussion and collaboration.

https://pirsa.org/C22033

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

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