- #1

- 135

- 4

## Main Question or Discussion Point

I am trying to understand the derivation of the Dirac adjoint. I understand the derivation of the following identities involving Spinors, the Gamma matrices and Lorentz transformations:

(S

s[Λ] = exp(Ω

s[Λ]

The part I'm having trouble with is showing that the last line is also equal to:

γ

Its probably simple but I'm having a mental block with it. Appreciate any help to get me going again.

(S

^{μν})^{†}= γ^{0}S^{μν}γ^{0}s[Λ] = exp(Ω

_{μν}S^{μν}/2)s[Λ]

^{†}= exp(Ω_{μν}(S^{μν}/2)^{†})The part I'm having trouble with is showing that the last line is also equal to:

γ

^{0}S[Λ]^{-1}γ^{0}Its probably simple but I'm having a mental block with it. Appreciate any help to get me going again.