Parallel Transport

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Latest Notes

Kartik Prabhu
replied to a post on www.math.columbia.edu with
I did a quick review in https://arxiv.org/abs/1511.00388v3 Some more physics-oriented ones: Y. Choquet-Bruhat, C. Dewitt-Morette, and M. Dillard-Bleick, Analysis, Manifolds and Physics, Part I: Basics. Y. Choquet-Bruhat and C. Dewitt-Morette, Analysis, Manifolds and Physics. Part II: 92 Applications. Some more mathematical ones: S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Volume I. Interscience Tracts in Pure and Applied Mathematics. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Volume II. Interscience Tracts in Pure and Applied Mathematics.
Kartik Prabhu
reposted a post on Twitter because
Latest in infrared finite scattering! https://arxiv.org/abs/2402.00102 Any non-trivial scattering in quantum gravity will produce non-trivial low frequency effects related to the production of gravitational memory. At null infinity, the memory manifests itself in the presence of unitarily inequivalent Hilbert space sectors each with a definite value of the memory. The memory is not Lorentz-invariant so these states with definite memory do not have a finite value of Lorentz charge operators (e.g. angular momentum). This was worked out by Ashtekar long ago. We show how to stitch together these memory states into Hilbert spaces that have a well-defined Lorentz charge. There are still many inequivalent Hilbert spaces, but now we have a large supply of states which include both the memory and Lorentz charges and can be used to do scattering. More to come…

Latest Articles

<href> in SVG

While creating an animated SVG logo for indietech.rocks we ran into a strange problem where the SVG would display in some browsers and not in others. The issue is the different ways browsers handle XML — yes SVG is XML! So here is the problem and its solution.

Placeholder Images

The size of my images changes fluidly with my responsive layout. Since the browser does not know their heights a priori, the space collapses while the images are still loading. Once the images load the entire page reflows and the rest of the content jumps around to make space for them. It would be much better if the space for the images was reserved from the start and, as a bonus, if some lower resolution version of the images displayed, while the images load. Here is how I do it.