Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 11.6.1

Quantum Electrodynamics — Robert Mann

Physics — Particle Physics · dirac-spinor-completeness-relations

Problem

Show for Dirac spinors

u(p)

and

v(p)

that

\sum_{i=\uparrow,\downarrow} u^{(i)}_a(p)\overline{u}^{(i)}_b(p) = \left(\not{p} + m\right)_{ab} \quad \text{and} \quad \sum_{i=\uparrow,\downarrow} v^{(i)}_a(p)\overline{v}^{(i)}_b(p) = \left(\not{p} - m\right)_{ab}