All Questions
4 questions
3
votes
1
answer
258
views
Symplectic orbits in projective Hilbert spaces are simply connected
Let $G$ be a connected Lie group and let $(\pi, \mathcal{H})$ be an irreducible unitary representation of $G$ on an infinite-dimensional Hilbert space $\mathcal{H}$. Denote by $\mathcal{H}^{\infty}$ ...
- 131
0
votes
1
answer
313
views
Symplectic structure on $Sym^kG^{\mathbb{C}} $
Let $G$ be a compact Lie group, and let $G^\mathbb{C}$ be its complexification.
I am looking for a symplectic structure (without use of coordinates) on
$$
Sym^kG^{\mathbb{C}},
$$
PS:Here $G^{\mathbb{...
user21574
3
votes
2
answers
589
views
How to deal with the singular reduction of the Hamiltonian n body problem?
I would like to consider the reduced Hamiltonian $n$ body problem, but am struggling with the angular momentum reduction seeing as the $SO(3)$ action is not free and the reduction is singular.
...
7
votes
1
answer
721
views
Generalization of Rigid Body Motion to arbitrary (compact) Lie Groups
The classical dynamics of a rigid body in three dimensions may be described as the motion of a point on a configuration space given by the Lie group $SO(3)$, governed by Euler's equations for rigid ...
- 295