I'm attending a course in Symplectic Mechanics and I have some problems in understanding something written in my lecture notes. We are in the following setting: let $Q$ be a manifold (of dimension ...
The mathematics of symplectic (as well as Hamiltonian) vector fields is something that has been quite clear to me for some time, but recently I have been thinking much more about what certain ...
We were given the following problem: show that $[A,[B,C]] + [B,[C,A]] + [C,[A,B]] = 0$ where $[A,[B,C]]$ et cetera are Poisson brackets. As I understand it this is a poisson bracket (where ...
I'm trying to motivate why a symplectic structure captures exactly the right structure one needs to do classical mechanics. The easiest part of this story goes like this: we need a procedure for ...
Consider a symplectic manifold $(M, \omega)$. Let us define a concept of a complete set of observables: A set of functions $f_i : M \to \mathbb R$ form a complete set of observables if any ...