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2009

Riemann Normal Coordinate expansions using Cadabra

Brewin, Leo

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Riemann normal coordinate expansions of the metric and other geometrical quantities, including the geodesic arc-length, will be presented.

All of the results are given to fifth-order in the curvature and were obtained using the computer algebra package Cadabra.

Riemann Normal Coordinate expansions using Cadabra · Around

Built on

“Riemannian Geometry”
Luther Eisenhart · 1926
Earlier work this paper cites.
“The volume of a small geodesic ball of a Riemannian manifold”
Alfred Gray · 1973
Earlier work this paper cites.
“Computer Calculation of Tensors in Riemann Normal Coordinates”
Yoshiyuki Yamashita · 1984
Earlier work this paper cites.
“Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations”
E. Calzetta, S. Habib and B.L. Hu · 1988
Earlier work this paper cites.
“Riemannian Geometry”
T.J. Willmore · 1996
Earlier work this paper cites.

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“Normal Coordinates in Kahler Manifolds and the Background Field Method”
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“Riemannian Geometry. A modern introduction, 2nd ed.”
Isaac Chavel · 2006
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“A tutorial on Cadabra”
Leo Brewin
Cited in the paper.

Then

“Introducing Cadabra: a symbolic computer algebra system for field theory problems”, 2007
Kasper Peeters · 2007
Later among the works it cites.
“A brief introduction to Cadabra: a tool for tensor computations in General Relativity”
Leo Brewin · 2010
Closest in time.
“The Cadabra v2.x home page”, 2017
Kasper Peeters · 2017
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“The Cadabra2 GitHub reporistory”, 2017
Kasper Peeters · 2017
Closest in time.
“Cadabra2: computer algebra for field theory revisited.”
Kasper Peeters · 2018
Closest in time.

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