- #1

Osiris

- 20

- 0

I guess it should be my mistake somewhere.

https://www.amazon.com/dp/0521670543/?tag=pfamazon01-20

On Page 30, for the derivation of EQ. (15.7.19), the nilpotency of BRST operator on the ghost for gauge transformation,

[tex]\delta _{\theta}s\omega_\alpha &=& - \frac{1}{2}C_{\alpha\beta\gamma}\delta_\theta(\omega_\beta\omega_\gamma)

&=&\frac{1}{4}\theta (C_{\alpha\beta\gamma}C_{\beta\delta\epsilon}\omega_\delta\omega_\epsilon\omega_\gamma ++ C_{\alpha\beta\gamma}C_{\gamma\delta\epsilon}\omega_\beta\omega_\delta\omega_\epsilon)=...

[/tex]

The plus "++" above, I suppose it should be "-" considering [tex]\omega[/tex] is an anticommuting ghost and the BRST operator is odd and acting from left. Steven also mentioned this in the paragraph below Eq. (15.7.19).

Did I miss any point here? Since then we would not have nilpotency of BRST operator on the ghost.

https://www.amazon.com/dp/0521670543/?tag=pfamazon01-20

On Page 30, for the derivation of EQ. (15.7.19), the nilpotency of BRST operator on the ghost for gauge transformation,

[tex]\delta _{\theta}s\omega_\alpha &=& - \frac{1}{2}C_{\alpha\beta\gamma}\delta_\theta(\omega_\beta\omega_\gamma)

&=&\frac{1}{4}\theta (C_{\alpha\beta\gamma}C_{\beta\delta\epsilon}\omega_\delta\omega_\epsilon\omega_\gamma ++ C_{\alpha\beta\gamma}C_{\gamma\delta\epsilon}\omega_\beta\omega_\delta\omega_\epsilon)=...

[/tex]

The plus "++" above, I suppose it should be "-" considering [tex]\omega[/tex] is an anticommuting ghost and the BRST operator is odd and acting from left. Steven also mentioned this in the paragraph below Eq. (15.7.19).

Did I miss any point here? Since then we would not have nilpotency of BRST operator on the ghost.

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