544 reputation
215
bio website robertfilter.net
location Jena, Germany
age 32
visits member for 3 years, 10 months
seen yesterday

If you like electrodynamic problems with solutions and their connections to current research, please visit www.problemsinelectrodynamics.com


Jan
6
asked $2\cdot\int_0^\infty \frac{a-u^2}{\left( u^2+\frac{a^2}{b-a}\right) \left(u^2+\frac{b^2}{b-a} \right) \sqrt{\cdots } }\mathrm {d}u $
Dec
22
answered How to check if transformation is affine?
Dec
12
comment Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?
@Raskolnikov: Thank you for the comment which pointed directly in the right direction. Nevertheless my experience in functional analysis on manifolds is very limited so I could not really grasp the idea. I think Willie Wong pointed out these lines of thought in a very explicit and decent way.
Dec
11
awarded  Scholar
Dec
11
accepted Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?
Dec
11
comment Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?
Thank you very much for your thoughtful and detailed answer. If I got you correctly, the notion only makes sense for the existence of a timelike killing vector, say $\partial_t$. This should imply that a time <> frequency FT only makes sense for stationary solutions in which the quotient manifold $M/\psi_t$ ($\psi_t$ being the local flux to $\partial_t$) exists. Hence, the FT is only feasible for dynamical field theories if the dynamics are independent from the (background) metric.
Dec
11
awarded  Supporter
Dec
11
awarded  Student
Dec
11
asked Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?
Dec
7
awarded  Teacher
Dec
6
answered Why study “curves” instead of 1-manifolds?