In Qed they replace the current vector [tex]J^{\alpha}[/tex] by [tex]ie\overline{\Psi}\gamma^{\alpha}\Psi[/tex]. I don't understand how this is done. I understand that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]J^{A\dot{A}}=J^{\alpha}{\sigma^{A\dot{A}}_\alpha}[/tex] but if [tex]J^{A\dot{A}}[/tex] is a rank two matrix then [tex]J^{A\dot{A}}=\psi^{A}\psi^{*\dot{A}}+\phi^{A}\phi^{*\dot{A}}[/tex]. So shouldn't [tex]J^{\alpha}[/tex] be written as something like

[tex]ie(\bar{\Psi}\gamma^{\alpha}\Psi +\bar{\Phi}\gamma^{\alpha}\Phi)[/tex]?

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

Dismiss Notice

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 spinor question

Loading...

Similar Threads for Dirac spinor question |
---|

A Positive and negative plane wave solutions of Dirac equation |

A Invariance of Dirac Lagrangian |

A Transformation of solutions of the Dirac equation |

A Transformation of Dirac spinors |

A Probability density of dirac spinors |

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