Philip A. LeMaitre

Research Interests: Quantum Machine Learning, Quantum Foundations, Artificial Intelligence, Quantum Gravity, Relativistic Quantum Information.

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It’s a big world out there, and there is so much to see and do, maybe a bit too much… While I will continue to be endlessly fascinated by our vast cosmos, it is sometimes difficult to know what events/initiatives are happening out there and where to look for resources. Luckily, I have compiled a list of current initiatives/institutions I am part of or am interested in, as well as links to courses and some research/course notes, and just general resources for those of you who want to get your feet wet in the theoretical physics aether. I hope you enjoy :)

Starter Pack

The theoretical physicist Gerard ‘t Hooft already has a very informative and comprehensive guide to becoming a theoretical physicist on their webpage, but I will try to give my own perspective coming from a different background and with a more contemporary twist.

English is the lingua franca of physics and much of academia, so you have to make sure you have a working knowledge of it and that you can prove this to any institutions where you want to study. The basics of the language are quite simple and you can usually pick up what you need through ingesting media or talking to people; AI has evolved rapidly to the point where it can really help you practice the language (or any language for that matter) as well. My advice is to not worry too much about perfecting your grammar or pronunciation since English is very forgiving on both fronts, just make sure you can be understood. Of course, to become a good writer you will need to know the language better.

Theory breathes through the language of mathematics, so you absolutely must start with the basics. Calculus, linear algebra, and proofs are the grammar of almost everything that comes later.

Some computer science knowledge is also handy to have, especially if you want to simulate models, test ideas numerically, or move anywhere near machine learning. You do not need to become a software engineer, but you should be able to make a computer do useful work for you. Getting familiar with languages such as Python or Julia is the best way to start since they are ubiquitous in physics and machine learning, plus they are also among the most human-readable languages. Many theorists also like to use Wolfram Mathematica or Maple, which are very useful symbolic mathematics programs with their own syntax, but beware they are both proprietary software.

Most theorists would discombobulate at the mention of this, and in many respects it is not necessary to be able to actively work on theoretical physics, but I think it is important that every good theorist have some grounding in philosophy. Questions about explanation, evidence, abstraction, ontology, and what counts as understanding show up constantly even when people pretend they do not. You often find researchers - and arguably all people - have heavy philosophical commitments and understated assumptions that are fueling their argumentation and/or worldview, so it helps to acknowledge and convey these clearly to engage with the community in a productive way. Not only this, but solid philosophical training allows you to better translate the contents of physical theories into intuition, so that you can better construct and reason about physical theories based on what you think (and what the evidence say) the world should be like, instead of forcing mathematics onto the description of nature.

Below I have listed some courses/subjects you should study - listed roughly in order - to have a solid foundation.

Courses

The Perimeter Institute of Theoretical Physics in Canada has a wonderful archive of all recorded talks and lectures given there called PIRSA which I urge you to take advantage of; they have material on almost any theoretical physics topic you can imagine. MIT and Stanford also post many of their excellent university course lectures on YouTube, which I also recommend. For the track leading up to university, Khan Academy is a wonderful platform to develop your foundation.

Mathematics Basics

This is where you learn how to calculate reliably and translate verbal problems into symbolic ones. The big ideas here are number sense, equations and inequalities, functions, geometric reasoning, and the habit of representing the same structure in several ways at once: algebraically, graphically, and verbally.

Computer Science Basics

You should come away from this stage knowing how to express a procedure precisely enough for a computer to execute it. Focus on variables, control flow, functions, data structures, debugging, plotting, and basic numerical experimentation; once machine learning enters the picture, ideas like optimization, generalization, overfitting, and data pipelines start to matter as well.

Philosophy Basics

Philosophy helps you get clearer on what a theory is claiming, what would count as evidence for it, and what sort of explanation you are actually after. The main background ideas here are existence and structure in metaphysics, justification and knowledge in epistemology, and validity, consequence, and formal representation in logic.

There is also an excellent introductory book series called “A Very Short Introduction to…” published by Oxford University Press, which covers all manner of philosophy topics (many other topics as well) in an accessible way. It is often a good jumping off point to discover the areas that interest you and where to look next.

Introductory Mathematics

This is the first genuinely university-style layer of mathematical maturity. You want to understand proof structure, limits, derivatives, integrals, vector spaces, eigenvalues, dynamical systems, and approximation schemes, because these are the tools that let physical models become analyzable rather than just intuitive.

Introductory Physics

Here the point is to build your physical intuition before the formalism gets too abstract. Learn how to think in terms of forces, fields, energy, equilibrium, conservation laws, and simple model systems, while also getting used to dimensional analysis and the practice of turning a messy physical situation into an idealized problem.

Intermediate Mathematics

At this stage you are expanding both breadth and rigor. The crucial concepts are multivariable change, rigorous convergence, probability distributions, Fourier-style thinking, linear operators, and the difference between exact analytic control and carefully justified approximation.

Intermediate Physics

This is where modern physics starts to feel like modern physics. You should get comfortable with fields and potentials, wave optics, Hilbert-space-based quantum thinking, Lorentz transformations, phase space, ensembles, and symmetry principles, since these ideas reappear almost everywhere later on.

Advanced Mathematics

These subjects are less universally required all at once, but each opens a major door in modern theory. Manifolds, continuity and compactness, holomorphic structure, infinite-dimensional vector spaces, measure, and symmetry groups all become natural language in quantum theory, relativity, field theory, and statistical mechanics.

Advanced Physics

By this point you are no longer just learning background; you are entering the conceptual neighborhoods where research actually lives. Expect operator methods, many-body systems, quantum correlations, relativistic spacetime structure, effective descriptions, and the interplay between symmetry, measurement, and emergent phenomena.

Graduate Physics

This is the level where different pillars of modern theory begin to overlap directly and research taste starts to matter. The central ideas are local symmetry, quantized fields, renormalization, spacetime curvature, information-theoretic constraints, and the challenge of reconciling the quantum and gravitational pictures of the world.

Research Notes

Here I will list some useful research notes that are freely available. I also have some more basic notes covering useful mathematical identities and basic properties plus physics unit conventions (but beware, it is a work in progress).

Broad Background Primers

  • Proofs, calculus, and linear algebra for theorists / notes
  • Probability, statistics, and stochastic intuition / notes
  • Mathematical methods for physicists / notes
  • Classical mechanics, fields, and variational thinking / notes
  • Quantum mechanics and operator methods / notes
  • Statistical physics and many-body reasoning / notes
  • Geometry, topology, and spacetime structure / notes
  • Computation, numerical methods, and scientific Python / notes

More Specific Topics

  • Conventions and identities for relativistic quantum theory / notes
  • Gaussian states, detectors, and correlation functions / notes
  • Hypergraphs, tensors, and many-body-inspired truncations / notes
  • Contextuality and nonclassical resources / notes
  • Unruh-DeWitt detectors and field-mediated interactions / notes
  • Relativistic quantum information primer / notes
  • Projective simulation and interpretable agents / notes

Mini-Explainers

I am starting to build short notebook-backed explainers for recurring ideas on the site. They are meant to sit between plain-language summaries and the more technical research material.

  • Mini-Explainers for short visual or computational explanations
  • Research for the papers, talks, posters, and lay summaries
  • Posts for topic-based browsing through the blog

Current Initiatives and Institutions

Many of these initiatives/institutions/hubs are tailored towards my own interests so don’t expect to find everything here.

Initiatives

Institutions

Hubs

Keep Exploring

If you came here for notes or demos, these are the fastest ways to branch into the rest of the site.

Research overview Jump to publications, talks, posters, and lay summaries of the main projects. Mini-Explainers Short notebook-backed explainers that sit between intuition and technical detail. Browse posts by topic Use the blog page to navigate through categories, tags, and year archives.