Mathematical Physics

During this semester (the first semester of 2010) I'm teaching a course on topics of Mathematical Physics (every friday, at 15:30h, at IME-USP, room B09). There will be a continuation of the course during the second semester. The course is for mathematicians and for graduate students in Mathematics (people who can handle things like manifolds, functional analysis, measure theory). There are no physics prerequisites. I will cover some basic material on Classical Mechanics (including Lagrangians and Hamiltonians on manifolds, conservation laws, simplectic manifolds and poisson brackets) and some basic material on Quantum Mechanics. On Quantum Mechanics, I will cover the standard formalism of states and observables (in terms of Hilbert spaces and self-adjoint operators), Schrödinger equation, and so on. Unlike typical courses on the subject, there will be critical discussion of what all that stuff means (that includes topics such as Bell's theorem and related results). We will present also Bohmian Mechanics, which is the simplest example of a Quantum Theory without observers. That is an example of a precisely formulated physical theory from which the standard quantum rules for predicting experiments emerge. I'm writing some notes for the course. The most recent version of the notes will be kept available here in pdf form (last update on the notes, may 27th, 2010).

Daniel V. Tausk