Lecture.8.Fermions and the Dirac Equation

# Lecture.8.Fermions and the Dirac Equation -...

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Fermions and the Dirac Equation In 1928 Dirac proposed the following form for the electron wave equation: 4 row column matrix 4x4 matrix 4x4 unit matrix The four μ matrices form a Lorentz 4 vector, with components, μ. That is, they transform like a 4 vector p, μ , y under Lorentz transformations between moving frames. Each μ is a 4x4 matrix.

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Pauli spinors:
The 0 and 1,2,3 matrices anti commute The 1,2,3, matrices anti commute with each other The square of the 1,2,3, matrices equal minus the unit matrix e square of the 0 matrix The square of the 0 matrix equals the unit matrix ll of the above can be summarized in the following expression: All of the above can be summarized in the following expression: Here g μ is not a matrix, it is a component of the inverse metric tensor . 4x4 unit matrix 4x4 matrices

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ith the above properties for the atrices one n show that if tisfies With the above properties for the matrices one can show that if satisfies the Dirac equation, it also satisfies the Klein Gordon equation. It takes some work.
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## Lecture.8.Fermions and the Dirac Equation -...

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