All Questions
11 questions
2
votes
0
answers
49
views
Lie group and symmetry concept for weak notions of surfaces
I am studying measure-theoretic and functional analytic notions of surfaces such as varifolds and, since my background comes from physics I am wondering whether there is a simiar concept such as Lie ...
- 21
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
7
votes
0
answers
501
views
intuitive connection between The KdV equations and the Virasoro bott group
I posted this on stack exchange but had no joy, perhaps someone here can answer : The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group....
- 979
12
votes
2
answers
849
views
Geodesics on $SU(4)$
Are the geodesics of the following metrics on $SU(4)$ known or easy (in a way not known to me!) to find?
In the adjoint representation, one can express the Killing form as a matrix and consider it as ...
- 2,099
1
vote
0
answers
324
views
Solving $T^2 = -\kappa\, \mathrm{Tr}\, (\log(e^{i T \hat{H}_0} \hat{O}) )^2$ equation
Is there a way to solve the equation: $T^2 = -\kappa\, \mathrm{Tr}\, (\log(e^{i T \hat{H}_0} \hat{O}) )^2$ for $T$?
Here $\kappa$ is an arbitrary positive constant, $\hat{H}_0 \in \mathfrak{su}(N)$ ...
- 2,099
6
votes
5
answers
2k
views
How to characterize Dirac's gamma matrices in differential geometry?
I want to understand what is the interpretation of Dirac gamma matrices in differential geometry. Basically, I am considering the Dirac matrices as 3-indexed tensors, which means a tensor with 1 ...
- 161
4
votes
0
answers
504
views
Local version of a slice (for a Lie group action)
Let $\Upsilon: G \times M \to M$ be a smooth action of a Lie group $G$ on a manifold $M$.
Isenberg and Marsden (1982) define a slice at $m \in M$ as a submanifold $S \subseteq M$ containing $m$ such ...
- 5,824
8
votes
1
answer
4k
views
Wedge Product of Lie Algebra Valued One-Form
I've been reading about the formal structure of gauge theories and am a little confused by the notation. Could someone clarify this for me?
Suppose that $A$ is a Lie algebra valued 1-form ...
- 827
13
votes
3
answers
2k
views
Software for Computing Baker-Campbell-Hausdorff
Does anyone have a recommendation for software which can efficiently calculate the Baker-Campbell-Hausdorff series in classical Lie algebras?
Right now, I have a problem which boils down to ...
- 1,138
10
votes
3
answers
4k
views
Is the Lie algebra-valued curvature two-form on a principal bundle P the curvature of a vector bundle over P?
I am an analyst struggling through some geometry used in physics.
Some background: For some Lie group $G$, let $P$ be a principal $G$-bundle over the smooth manifold $M$. Let $\omega$ be a connection ...
- 1,771
77
votes
7
answers
21k
views
What is the symbol of a differential operator?
I find Wikipedia's discussion of symbols of differential operators a bit impenetrable, and Google doesn't seem to turn up useful links, so I'm hoping someone can point me to a more pedantic discussion....
- 54.6k