Monthly Archives: May 2024

The purpose of this post is to review the classical theory of rigid body dynamics by working through a few illustrative problems in that regard. Problem #\(1\): What defines a rigid body? What is an immediate corollary of this? Solution … Continue reading →

A ChatGPT thesaurus of all the synonyms of “propagator” across different disciplines: Problem #\(1\): What is the retarded propagator of a quantum particle with Hamiltonian \(H\) in nonrelativistic quantum mechanics? Solution #\(1\): At its heart, the “retarded” part should make … Continue reading →

Newton’s second law in its most basic form states that for a single point mass, \(\dot{\textbf p}=\textbf F\) in any inertial frame. Combining this with Newton’s third law (antisymmetry of forces \(\textbf F_{i\to j}=-\textbf F_{j\to i}\), similar to many other … Continue reading →

The purpose of this post is to appreciate that the familiar idea of non-interacting particles from e.g. statistical mechanics manifests in the context of QFT as a free quantum field theory. Problem #\(1\): What defines a free classical field theory? … Continue reading →

Consider an arbitrary worldline \(\{(t,\textbf x)\}\) of a classical system of particles in configuration spacetime. In general, this worldline need not correspond to any physical/on-shell trajectory; it can be as wildly off-shell as one likes, the only caveat being that … Continue reading →

Problem: What is the defining property of the (Cauchy) stress tensor (field) \(\sigma(\textbf x,t)\) of a material. Solution: The idea is that if one wants to find the stress vector (also called traction) \(\boldsymbol{\sigma}\) acting on a plane with unit … Continue reading →