Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 11.6.6

Quantum Electrodynamics — Robert Mann

Physics — Particle Physics · dirac-bilinear-lorentz-properties

Problem

Verify the following Lorentz transformation properties: ψ‾′ψ′=ψ‾ψ\overline{\psi}'\psi' = \overline{\psi}\psi ψ‾′γ5ψ′=det⁡(Λ) ψ‾γ5ψ\overline{\psi}'\gamma^5\psi' = \det(\Lambda)\,\overline{\psi}\gamma^5\psi ψ‾′γμψ′=Λ  νμ ψ‾γνψ\overline{\psi}'\gamma^\mu\psi' = \Lambda^\mu_{\;\nu}\,\overline{\psi}\gamma^\nu\psi ψ‾′γμγ5ψ′=det⁡(Λ) Λ  νμ ψ‾γνγ5ψ\overline{\psi}'\gamma^\mu\gamma^5\psi' = \det(\Lambda)\,\Lambda^\mu_{\;\nu}\,\overline{\psi}\gamma^\nu\gamma^5\psi for a Dirac spinor ψ\psi.

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