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.
Torre, Charles G., "How to Create a Two-Component Spinor" (2012). How to... in 10 minutes or less. Paper 2.
Additional FilesHowToCreateATwoComponentSpinor.pdf (199 kB)
HowToCreateATwoComponentSpinor.mw (191 kB)