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christodouloum

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Hi, I am learning what is going on with ghost fields in string theory. Does anyone know where I can find the basics for the brs (brst) operator? Specifically I need help with the following calculation. I have for the action of the brs operator on a ghost field and on the metric

[tex]s \xi^\alpha = \xi^\beta \partial_\beta \xi^\alpha [/tex]

[tex] s g_{\alpha\beta}=\Omega g_{\alpha\beta} + L_{\xi} g_{\alpha\beta}[/tex]

Omega is the Weyl field and L_xi the killing derivative.

I am trying to show explicitly that s^2 is zero when acting on the fields. I cannot show it for the ghost field or for the Weyl field Omega for which being a scalar the brs operator acts as

[tex]s \Omega = \xi^{\alpha} \partial_{\alpha} \Omega[/tex]

I believe it has to do with considering the ghost field as grassmann numbers and exploiting some property but I could not see what is going on only from the basic property x^2=0 and x1 x2=-x2 x1.

[tex]s \xi^\alpha = \xi^\beta \partial_\beta \xi^\alpha [/tex]

[tex] s g_{\alpha\beta}=\Omega g_{\alpha\beta} + L_{\xi} g_{\alpha\beta}[/tex]

Omega is the Weyl field and L_xi the killing derivative.

I am trying to show explicitly that s^2 is zero when acting on the fields. I cannot show it for the ghost field or for the Weyl field Omega for which being a scalar the brs operator acts as

[tex]s \Omega = \xi^{\alpha} \partial_{\alpha} \Omega[/tex]

I believe it has to do with considering the ghost field as grassmann numbers and exploiting some property but I could not see what is going on only from the basic property x^2=0 and x1 x2=-x2 x1.

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