The Beauty of the Feynman Path Integral
For all the news talking about quantum theory, most people don’t know or understand what the theory actually says. In fact, it takes years to understand it because it is not only very complex, but it rests on centuries of classical physics for its vocabulary. You have to understand all of classical mechanics to understand quantum mechanics. You have to understand classical field theory and statistical mechanics of fields to understand quantum field theory. Not to mention operator theory and Hilbert spaces.
There are quite a few descriptions of the Standard Model of quantum physics. This model includes all the particles that we know exist, all the forces, and how they all fit together. This is not one of those descriptions. What I want to talk about is more fundamental than that.
Ultimately, quantum theory is concerned with fields. There are spinor fields, fields of gauge bosons, Higgs field, and so on. All these fields combine in various ways to create the Standard Model.
There are two general approaches to quantum theory, one is via field operators, which are kind of like little mathematical machines that act on infinite dimensional vectors which represent particles and forces.
The other way is what Richard Feynman did his Ph.D. thesis on back in the 1940s, called the Feynman Path Integral.
