Quantum Field Theory and the Standard Model by Schwartz M.D. z-lib.org · Problem 10.3

Spinors — Schwartz M.D. z-lib.org

Physics — QFT · weyl-spinor-sigma-matrix-identities

Problem

Derive Eqs. (10.141) and (10.142): (a)

g_{\mu\nu}\sigma^\mu_{\alpha\dot{\alpha}}\sigma^\nu_{\beta\dot{\beta}} = 2\varepsilon_{\alpha\beta}\varepsilon_{\dot{\alpha}\dot{\beta}}

, (b)

\varepsilon_{\alpha\beta}\varepsilon_{\dot{\alpha}\dot{\beta}}\sigma^{\mu\,\beta\dot{\beta}} = \bar{\sigma}^\mu_{\alpha\dot{\alpha}}