Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 11.6.2

Quantum Electrodynamics — Robert Mann

Physics — Particle Physics · dirac-helicity-eigenstates

Problem

Find spinors

u

that satisfy

(\gamma^\mu p_\mu - m)\,u(p) = 0

that have positive energy and that are eigenstates of the operator

\hat{p}\cdot\vec{S}

where

\hat{p}

is the unit vector of the 3-momentum of the spinor and

\vec{S} = \frac{\hbar}{2}\vec{\Sigma} = \frac{\hbar}{2}\begin{pmatrix} \vec{\sigma} & 0 \\ 0 & \vec{\sigma} \end{pmatrix}

is the spin angular momentum operator.