Principles of Quantum Mechanics · Problem 20.14

The Dirac Equation — R. Shankar

Physics — Quantum Mechanics · dirac-equation-helicity

Problem

The helicity operator is defined as h=Σ⋅p^h = \boldsymbol{\Sigma}\cdot\hat{\mathbf{p}} where p^=p/∣p∣\hat{\mathbf{p}} = \mathbf{p}/|\mathbf{p}|. Show that helicity commutes with the free-particle Dirac Hamiltonian and find the helicity eigenspinors. Show that for massless particles helicity is Lorentz invariant.

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