Homotopico

I have had conflicting feelings about using AI, even before I started using it extensively. These feelings and thoughts have been simmering in my heart and head for a while now, but a few days ago, reading about how the U.S. military used AI to identify targets in Iran, followed by the news that *someone* (not Israel, not Iran) bombed an element...

Come along and watch as I slowly descend into madness trying to understand what Geometric Quantization is, and why anyone would care about it.

Wherein I discuss some pretty pictures I made with the computer and the mathematics behind them.

What happens if we add a particle to an electromagnetic field? What does it look like in the quantum case? What role do the potentials play in the evolution of the particle?

I'm so tired of sitting for two (even three!) hours in a lecture hall, paying attention, trying to keep up, only to have to review absolutely everything at home. Can we do better?

This is the first post in a series that tries to discover what a gauge field is. The best place to begin is in the easiest gauge theory, namely electromagnetism.

Have you ever had a k-form but wanted a (n-k)-form? Do you have a metric? Well you're in luck! Here we tell you how the Hodge star operator lets you pass from one to the other.

Here we will construct state spaces with an *arbitrary number of particles*, instead of a *fixed* number of particles. We first focus on a 2-state system, for example polarization of photons or spin-(1/2).