Skip to main content

Some recent talks (Summer 2024)

My posting frequency has decreased since grad school, since while I'm spending about as much time learning as I always have, much more of my pedagogy these days ends up in papers. But I've given a few pedagogically-oriented talks recently that may be of interest to the people who read this blog.

  1. I gave a mini-course on "the algebraic approach" at Bootstrap 2024. The lecture notes can be found here, and videos are available here. The first lecture covers the basic tools of algebraic quantum field theory; the second describes the Faulkner-Leigh-Parrikar-Wang argument for the averaged null energy condition in Minkowski spacetime; the third describes recent developments on the entropy of semiclassical black holes, including my recent paper with Chris Akers.
  2. Before the paper with Chris was finished, I gave a general overview of the "crossed product" approach to black hole entropy at KITP. The video is available here. The first part of the talk goes back in time to the history of thermodynamics and classical statistical mechanics, and the rest of the talk describes modern developments in a far-view historical context.
  3. At UChicago, I gave a talk (video here) about my paper "Analyticity and the Unruh effect," which is about geometrically local modular flow. The talk includes a gentle introduction to the theory of modular flow, and an exposition of some useful analytical techniques for studying modular flow in quantum field theory.

Comments

Popular posts from this blog

Envelopes of holomorphy and the timelike tube theorem

Complex analysis, as we usually learn it, is the study of differentiable functions from $\mathbb{C}$ to $\mathbb{C}$. These functions have many nice properties: if they are differentiable even once then they are infinitely differentiable; in fact they are analytic, meaning they can be represented in the vicinity of any point as an absolutely convergent power series; moreover at any point $z_0$, the power series has radius of convergence equal to the radius of the biggest disc centered at $z_0$ which can be embedded in the domain of the function. The same basic properties hold for differentiable functions in higher complex dimensions. If $\Omega$ is a domain --- i.e., a connected open set --- in $\mathbb{C}^n$, and $f : \Omega \to \mathbb{C}^n$ is once differentiable, then it is in fact analytic, and can be represented as a power series in a neighborhood of any point $z_*$, i.e., we have an expression like $$f(z) = \sum a_{k_1 \dots k_n} (z_1 - z_*)^{k_1} \dots (z_n - z_*)^{k_n}.$$ The

The stress-energy tensor in field theory

I came to physics research through general relativity, where the stress energy tensor plays a very important role, and where it has a single unambiguous meaning as the functional derivative of the theory with respect to metric perturbations. In flat-space quantum field theory, some texts present the stress tensor this way, while some present the stress tensor as a set of Noether currents associated with spatial translations. These definitions are usually presented as being equivalent, or rather, equivalent up to the addition of some total derivative that doesn't affect the physics. However, this is not actually the case. The two stress tensors differ by terms that can be made to vanish classically, but that have an important effect in the quantum theory. In particular, the Ward identities of the two different stress tensors are different. This has caused me a lot of grief over the years, as I've tried to compare equations between texts that use two different definitions of the

Stone's theorem

 Stone's theorem is the basic result describing group-like unitary flows on Hilbert space. If the map $t \mapsto U(t)$ is continuous in a sense we will make precise later, and each $U(t)$ is a unitary map on a Hilbert space $\mathcal{H},$ and we have $U(t+s)=U(t)U(s),$ then Stone's theorem asserts the existence of a (self-adjoint, positive definite, unbounded) operator $\Delta$ satisfying $U(t) = \Delta^{it}.$ This reduces the study of group-like unitary flows to the study of (self-adjoint, etc etc) operators. Quantum mechanically, it tells us that every group-like unitary evolution is generated by a time-independent Hamiltonian. This lets us study very general symmetry transformations in terms of Hamiltonians. The standard proof of Stone's theorem, which you'll see if you look at Wikipedia , involves trying to make sense of a limit like $\lim_{t \to 0} (U(t) - 1)/t$. However, I have recently learned of a beautiful proof of Stone's theorem that works instead by stud