Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Keyword
Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
How To Make Tetrads, Charles G. Torre
How To Make Tetrads, Charles G. Torre
How to... in 10 minutes or less
This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.
The Kretschmann Scalar, Charles G. Torre
The Kretschmann Scalar, Charles G. Torre
How to... in 10 minutes or less
On a pseudo-Riemannian manifold with metric g, the "Kretschmann scalar" is a quadratic scalar invariant of the Riemann R tensor of g, defined by contracting all indices with g. In this worksheet we show how to calculate the Kretschmann scalar from a metric.
How To Find Killing Vectors, Charles G. Torre
How To Find Killing Vectors, Charles G. Torre
How to... in 10 minutes or less
We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.
How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson
How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to compute the Levi decomposition of a Lie algebra in Maple using the command LeviDecomposition. A worksheet and corresponding PDF can be found below.
How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile
How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile
How to... in 10 minutes or less
We show how to create a Jordan algebra in Maple using the commands AlgebraLibraryData and AlgebraData.
How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile
How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile
How to... in 10 minutes or less
We show how to create the quaternion and octonion algebras with the DifferentialGeometry software. For each algebra, there is a split-form also available.
How To Create A Two-Component Spinor, Charles G. Torre
How To Create A Two-Component Spinor, Charles G. Torre
How to... in 10 minutes or less
Let (M, g) be a spacetime, i.e., a 4-dimensional manifold M and Lorentz signature metric g. The key ingredients needed for constructing spinor fields on the spacetime are: a complex vector bundle E -> M ; an orthonormal frame on TM ; and a solder form relating sections of E to sections of TM (and tensor products thereof). We show how to create a two-component spinor field on the Schwarzschild spacetime using the DifferentialGeometry package in Maple. PDF and Maple worksheets can be downloaded from the links below.
How To Create A Lie Algebra, Ian M. Anderson
How To Create A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.