Isotropic Spinors

A spinor is, for my purpose here, just a two-dimensional complex (or real) vector. An Isotropic Spinor is a nonzero spinor whose symplectic "magnitude" is zero. How this is done is explained in the papers. The great advantage of using isotropic spinors is that they can greatly reduce the length of proofs (especially in the paper on second-order linear differential equations), thereby allowing the reader to not get so bogged down in the details to be able to see the bigger picture.

Warning: I'm in the process of standardizing how I lower upper index spinors to lower index spinors. It may still vary depending on which paper you are reading.

2nd-order Differential Equations with Spinors (72)

This paper is easily the coolest of the group, in my opinion. It would help the reader to know some theory of second-order linear differential equations before tackling this paper. Also, some of the topics get mathematically involved, but for the more advanced readers, they should be welcome presentations of the Variation of Parameters, Sturm-Liouville theory, and Green's Functions. On the other hand, there is nothing accomplished in this paper that cannot be done by standard methods of linear algebra.

Proof that ∂μJμ = 0 in a QFT Problem Using Isotropic Spinors (6)

2X2 matrices and 1st-order DEQ with Spinors (53)

Ceva's Theorem with Isotropic Spinors 7

Pappus's Theorem with Isotropic Spinors 9

Standard Triangle Theorems with Isotropic Spinors 15