Griffiths Introduction to Elementary Particles · Problem 7.13

Electrodynamics of Quarks and Hadrons — David J. Griffiths

Physics — QFT · adjoint-spinors-dirac-equation

Problem

Show that the adjoint spinors

\bar{u}^{(1,2)}

and

\bar{v}^{(1,2)}

satisfy the equations

\bar{u}(\gamma^\mu p_\mu - mc) = 0, \qquad \bar{v}(\gamma^\mu p_\mu + mc) = 0

[Hint: Take the transpose conjugate of equations (7.34) and (7.51); multiply from the right by

\gamma^0

, and show that

(\gamma^\mu)^\dagger\gamma^0 = \gamma^0\gamma^\mu