# Dirac Equation for Massive 2-Spinors

It is possible to write an equation for 2-spinors that properly yields the Klein-Gordon equation when squared AND contains elements for a rest energy. Here is the solution:

The sigma are the Pauli matrices with the zero element just being the identity. We can use some basic math to derive the following from equation 1:

Here are some definitions of terms:

In this way, the rest energy acts as a sort of coupling between the spinor and it’s own charge conjugate. We can solve this equation in free space by doing the following:

Plugging this into equation 1 gives the following 4 equations for the variables A, B, C, and D:

This, like the Dirac equation, has 4 possible solutions: