Question

1. Prove that the matrices are hermitian or anti-hermitian.

2. Prove that in order for the Dirac equation to be covariant (i.e., form-invariant) under the Lorentz group of trans formations with the constraint that the gamma-matrices are unchanged, the following relation must hold:

$L_{v}^{\mu}\gamma ^{v}=S^{-1}(L)\gamma ^{\mu}S(L)$,

where $L_{v}^{\mu}$ is the Lorentz-transformation matrix for the 4- vectors (x'=Lx) and S is a unitary matrix that transforms the spinor as $\varphi '(x')=S(L)\varphi (x)$

Answer 1

イし ん! S (L 0 Now Quac S (L) γ Scanned with Camscanner