Griffiths Introduction to Elementary Particles · Problem 7.17

Electrodynamics of Quarks and Hadrons — David J. Griffiths

Physics — QFT · gamma-matrix-algebra

Problem

(a) Express

\gamma^\mu\gamma^\nu

as a linear combination of

1

\gamma^5

\gamma^\mu

\gamma^\mu\gamma^5

, and

\sigma^{\mu\nu}

. (b) Construct the matrices

\sigma^{12}

\sigma^{13}

, and

\sigma^{23}

[eq. (7.69)], and relate them to

\Sigma^1

\Sigma^2

, and

\Sigma^3

[eq. (7.48)].