Dirac Spinor - Derivation From Dirac Equation

Derivation From Dirac Equation

The Dirac equation has the form

In order to derive the form of the four-spinor we have to first note the value of the matrices α and β:

These two 4×4 matrices are related to the Dirac gamma matrices. Note that 0 and I are 2×2 matrices here.

The next step is to look for solutions of the form

,

while at the same time splitting ω into two two-spinors:

.

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