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I'm looking for topics in elementary QFT (canonical quantization, path integrals, representations of the Poincaré group, and perturbative calculations) that intersect with applications of standard quantum mechanics, such as quantum information theory or the theory of open systems. Bonus points if they are suitable for a short (~ 30/45 min.) presentation, and can be understood (at least at a basic level) from scratch without much knowledge of the non field-theoretic aspects (apart from elementary QM).

Some possibilities I've thought of include open electrodynamics (which is mostly about density matrix theory for QED and the study of coherence in electromagnetic processes), and information field theory (a topic I know little about, but seems promising even though there aren't many good resources online). I've also found some articles dealing with entropic functionals in QFT, but they seemed way too specific and mathematically convoluted for my purposes.

Ideally, I would like some kind of reference —such as an article or a textbook chapter — along with the suggestion that is as self-contained as possible.

I'm not really sure if this kind of questions is permitted on the site, please be kind with the downvote button!

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  • $\begingroup$ Question is a little vague...there's also little you can do in QFT without a fair amount of machinery. If this is for a school presentation you could probably just review the Wigner classification of Poincare representations. $\endgroup$ May 28, 2021 at 0:56

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John McGreevy has an excellent collection of lecture notes revolving around QFT. Much of the material is more advanced, but I'll highlight two items that might be suitable for your audience:

  1. Physics 239/139: Quantum information is physical (link to pdf)

  2. Physics 239a: Where do quantum field theories come from? (link to pdf)

The first item addresses the information-theory theme that was mentioned in the question. It doesn't revolve around quantum field theory, but it does make some connections. Here are some highlights from the introduction:

This is a special topics course directed at students interested in theoretical physics; this includes high-energy theory and condensed matter theory and atoms-and-optics and maybe some other areas, too. ... The subject will be ideas from information theory and quantum information theory which can be useful for quantum many body physics. ... In case it isn’t obvious, I want to discuss these subjects so I can learn them better. For some of these topics, I understand how they can be (and in many cases have been) useful for condensed matter physics or quantum field theory, and I will try to explain them in that context as much as possible. ... If you are worried about your level of quantum mechanics preparation, do Problem Set 0.5.

By the way, the subject that this excerpt calls "quantum many body physics" is a subset of QFT in the broad sense. (Related: What is the difference between many body theory and quantum field theory methods in condensed matter?)

The second item revolves around the theme that QFTs can often be regarded as low-resolution limits of lattice systems. Here's an excerpt from the introduction:

we will study quantum field theories which can be constructed by starting from systems with finitely many degrees of freedom per unit volume, with local interactions between them. Often these degrees of freedom will live on a lattice and perhaps could arise as a model of a solid. So you could say that the goal is to understand how QFT arises from condensed matter systems. ... An important goal for the course is demonstrating that many fancy phenomena precious to particle physicists can emerge from very humble origins in the kinds of (completely well-defined) local quantum lattice models we will study. Here I have in mind: fermions, gauge theory, photons, anyons, strings, topological solitons, CFT, and many other sources of wonder I’m forgetting right now.

Virtues of this approach to QFT include:

  • It bridges the gap between condensed-matter physics and relativistic particle physics.

  • Lattice models are mathematically well-defined using only elementary math (nothing fancy), which helps make QFT less intimidating. In fact, lattice models provide the only known mathematically-unambiguous constructions of several models relevant to particle physics, including QCD. (You might consider showing figure 15.7 from the Particle Data Group's 2020 review of the quark model (link to pdf). It shows the spectrum of hadrons obtained numerically from lattice QCD, which can help cure the QFT-is-about-Feynman-diagrams mindset.)

  • The low-resolution limits of lattice models often exhibit emergent symmetries and particles (see Symmetry and Emergence) and other phenomena that were not at all evident in the high-resolution formulation. This can be profoundly inspiring. It's one of the themes that got me hooked on QFT.

McGreevy's notes are designed to cover entire courses, but they include material that I think could be used to build an accessible 30-45 minute presentation. The hardest part might be deciding which material to include.

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