This is probably a stupid question, but when I apply the Euler-Lagrange equation to the Lagrangian density of the Dirac field I get for the conjugate field(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\bar{\psi} (-i \partial_\mu \gamma^{\mu} -m) = 0[/tex] (derivative acts to the left).

But when I take a hermitian conjugate of the Dirac equation for the field I get an extra [tex]\gamma^0[/tex]:

[tex]0 = \left[ (i \partial_\mu \gamma^{\mu} -m)\psi \right]^\dagger = \psi^\dagger (-i \partial_\mu (\gamma^{\mu})^\dagger -m) = \psi^\dagger (-i \partial_\mu \gamma^0 \gamma^{\mu} \gamma^0 -m) = \psi^\dagger \gamma^0(-i \partial_\mu \gamma^{\mu} \gamma^0 -m) = \bar{\psi} (-i \partial_\mu \gamma^{\mu} \gamma^0 -m)[/tex].

What am I missing?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dirac equation for the conjugated field

**Physics Forums | Science Articles, Homework Help, Discussion**