Lecture Notes

When teaching a course I usually write up lecture notes to cover the material as I do in class. These are meant as complements to the class texts. Two of them eventually became books published by Cambridge University Press.

The most polished of these are listed below, and several others (on various aspects of Quantum Field Theory) are 90% done and will appear as they become presentable. Exerpts (the first 6 chapters, including the full Table of Contents) of the two books are also included, to give potential buyers a taste of what the rest of the book is like.

The Standard Model: A Primer

Introduction to the Standard Model and Beyond

These notes use the Standard Model of particle physics as a vehicle for learning quantum field theory. The first two chapters quickly summarize several useful facts about relativistic quantum field theories for particles with spins 0, 1/2 and 1, and then outlines the Standard Model’s lagrangian and symmetry properties. After a whirlwind reminder about decays, cross sections and scattering in chapter 3, chapters 4-6 give a first-principles development of Feynman diagrams and their use to calculate decays and scattering rates for processes of practical interest in particle physics.

Advanced undergraduate and introductory graduate level (written for Physics 610A offered at McGill in Fall during the 1990s, but revised and updated after the discovery of the Higgs boson. Full book published by Cambridge University Press)

Introduction to Effective Field Theory

Thinking Effectively about hierarchies of scale

These notes describe techniques developed to exploit hierarchies of scale when analyzing physical problems. These methods also underpin the modern theoretical understanding of renormalization and emergence. To emphasize the universality of the methods topics are drawn from relativistic particle physics, gravity and string theory as well as non-relativistic atomic systems, condensed matter physics and open systems. The first six chapters contain the main conceptual tools used in all of the later applications, including applications to scattering processes, classical time evolution and boundary effects. (See here for the references and index.)

Graduate level (written for Physics 7A03 and other graduate courses offered at McMaster University and Perimeter Institute, as well as for various international summer schools, throughout the 2010s. Full book published by Cambridge University Press)

Effective Field Theories in Inflationary Cosmology

These notes have two aims. The first is to provide a whirlwind introduction to Hot Big Bang cosmology and to inflationary proposals aimed at accounting for the Hot Big Bang’s otherwise peculiar initial conditions. The notes start by introducing the background evolution and then move on to the properties of fluctuations about this background. The goal is to sketch the evidence for (and properties of) primordial fluctuations as observed in cosmology, and to describe how inflation explains these fluctuations in terms of quantum fluctuations in the much earlier universe.¬† The second aim is to describe the central role played throughout by Effective Field Theory methods, both for gravity in particular and for cosmological applications in particular.

Graduate level (written for the 2017 Summer School on Effective Field Theory in Particle Physics and Cosmology in Les Houches France, whose proceedings are published by Oxford University Press).

Tools of Mathematical Physics:

PDEs, ODEs, Analytic Continuation, Special Functions, Sturm-Liouville Problems and All That

These notes use boundary value problems for linear partial differential equations as a vehicle for describing the properties of ordinary differential equations; series solutions; special functions; some complex variable techniques; and Sturm-Liouville problems. Perhaps the main novelty of the presentation is to treat special functions as particular instances of the Hypergeometric functions, rather than as a series of unrelated special cases to be understood from scratch for each problem (as is often the traditional approach in undergraduate courses). This allows a unified treatment since these are the most general solutions to a class of problems that frequently arise in theoretical physics.

Undergraduate level (written for Physics 355A offered at McGill in Fall 1990)

Introduction to Quantum Field Theory: from Schrodinger to Feynman

These notes are meant as an introductory course on Quantum Field Theory, with the target audience being upper year undergraduates (the the second half is also appropriate for introductory graduate classes). The development starts with a discussion of multi-particle systems in nonrelativistic quantum mechanics and how to treat interactions that change the number of particles. Creation and annihilation operators are defined and applied to non-relativistic systems to explore second-quantized Schrodinger fields and Bose-Einstein condensation. Photons are introduced by quantizing the electromagnetic field and used to describe simple photon-atom interactions. The general role of symmetries in quantum mechanics is studied and applied to the Poincare transformations of special relativity, leading to the origins of antiparticles and the spin-statistics connection. Relativistic tools like canonical quantization and path-integral methods are developed and applied to simple relativistic fields and to quantum electrodynamics. The initial nonrelativistic discussions are independent of the later relativistic ones, so each half can be done separately.

Undergraduate level (written for Physics 4Q03/6Q03 offered at McMaster in winter 2019 and 2021). The graduate final chapters overlap with Physics 745 offered at McMaster and Perimeter Institute. These notes are not yet complete.

General Relativity: an Introduction for Undergraduates

These notes are meant as an introductory course on General Relativity, starting with the evidence for the proposal that gravitational phenomena in the solar system can be captured by the physics of curved spacetime and continuing to the discussion of Einstein’s field equations and their applications to more extreme environments. Among the topics covered are black holes, gravitational waves, relativistic stars, gravitational lensing and cosmology.

Undergraduate level (written for Physics 3A03 offered at McMaster in winter 2009)

Cosmology: the Notes

These notes are meant as an introductory course on Cosmology, starting with the the kinematics and dynamics of an expanding universe and continuing to the discussion of the thermodynamics and statistical mechanics of Big Bang cosmology. This includes a discussion of primordial relics and the merits of an early period of accelerated expansion. The final sections describe simple fluctuations about the cosmological background and provide a cartoon of the formation of large-scale structure.

Undergraduate and introductory graduate level (written for Physics 789 offered at McMaster in winter 2005)

Nuclear & Particle Physics: the Notes

These notes are meant as an introductory course on Nuclear and Particle Physics, starting with the discovery of the electron and proton and continuing through to the structure of nuclei, the discovery of the particle zoo and the advent of the Standard Model of Particle Physics. The course focuses on observational evidence and calculational tools, with the most important of the latter being classical and quantum scattering calculations. The notes close with a very brief introduction to the ideas of quantum field theory.

Undergraduate level (written for Physics 4A03 offered at McMaster in winter 2016; currently used for Physics 4E03 at McMaster)

Quantum Gravity in Everyday Life

GREFT: General Relativity as an Effective Field Theory

These provide an introduction to the Effective Field Theory that describes  how to merge gravity and quantum mechanics, at least at the low energies and large distances that are relevant for practical observations. This is done by appreciating that General Relativity has a natural interpretation as the leading part of a general low-energy Effective Field Theory of gravity (or GREFT for short). The tools described are pertinent to the low-energy limit of any system, but the notes focus on the issues that arise once these are applied to the study of gravity.

Introductory graduate level (written as a review for Living Reviews of Relativity in 2003)

The Cosmological Constant Problem

Why it’s Hard to get Dark Energy from Micro-Physics

These provide an introduction to the Cosmological Constant Problems, and to problems of `technical naturalness’ more generally. The Cosmological Constant Problem is the main obstacle to the current understanding of Dark Energy, which at face value looks precisely like what one would expect if the vacuum had nonzero energy density. Although this seems a very simple and effective description, there is no known theory of micro-physics for which all agree that this description seems to work. What is the Big Deal and why is describing Dark Energy so hard? Read the notes to find out!

Graduate level (written for the 2013 Summer School on Post-Planck Cosmology in Les Houches France, whose proceedings are published by Oxford University Press).