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asked Axiom of choice in proof of Wigner's theorem?
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Jan
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revised Geometric algebra approach to Lorentz group representations
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Jan
22
asked Geometric algebra approach to Lorentz group representations
Jan
22
comment Interpreting the scalar curvature in a semi-Riemannian manifold
@emiliocba I'm afraid I don't see it. A hyperbolic space is an example of a Riemannian manifold, isn't it? The scalar curvature may be negative, but the metric is still positive definite.
Jan
22
asked Interpreting the scalar curvature in a semi-Riemannian manifold
Dec
27
revised examples of 'continuous bases of functions,' like the Fourier transform
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Dec
27
asked examples of 'continuous bases of functions,' like the Fourier transform
Dec
23
comment Alternate definition of a 'geodesic ball'
I will look into the numerical factor. Unfortunately that doesn't account for the discrepancy. I added an appendix to my original post to explain the problematic terms I am finding in my calculation of $Vol(B_{alt})$.
Dec
23
awarded  Editor
Dec
23
revised Alternate definition of a 'geodesic ball'
added Appendix
Dec
23
comment Alternate definition of a 'geodesic ball'
Thanks for your reply. With this correction, do you think $B = B_{alt}$? I'm still not sure, for the following reason. A standard result I have seen is that the volume of a geodesic ball in two dimensions is $\pi \epsilon^2 [1 - (R / 48) \epsilon ^2 + O(\epsilon^4) ]$, where $R$ is the scalar curvature. I calculated the volume using the second definition ($B_{alt}$) in the special case of a diagonal metric and found terms that could not possibly occur in the scalar curvature. Changing $\epsilon$ to $\epsilon^{1/2}$ in my calculation does not make it match the standard result.