- #1
Jim Kata
- 197
- 6
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
[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]?
[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]?