Student Friendly Introduction to QFT · Problem 22

Spinors: Spin ½ Fields

Physics — QFT · euler-lagrange-dirac-lagrangian

Problem

Prove to yourself that for

n = 1

in the Euler-Lagrange equation applied to the Dirac Lagrangian density

\mathcal{L}_0^{1/2} = \bar{\psi}(i\gamma^\alpha \partial_\alpha - m)\psi

, we get the Dirac equation, and for

n = 2

, we get the adjoint Dirac equation.