- #1
earth2
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Hi guys,
i'm studying Conformal Field Theory using the big yellow book by Senechal et al. So far everything has been a smooth ride. I'm a bit stuck at the point where they derive the 2- and 3-point correlator for spinless fields.
Based on invariance under rotations and translations the correlator should depend only on the relative coords of the quasi primary fields and moreover - because of scaling invariance - this dependence should be of the type
[tex] f(|x_1-x_2|)\sim \lambda^{\Delta_1+\Delta_2}f(\lambda|x_1-x_2|)[/tex] where λ is the scaling and Δ the conformal weight.
But then those guys say that this is nothing but
[tex]\langle \phi(x_1)\phi(x_2)\rangle \sim \frac{1}{|x_1-x_2|^{\Delta_1+\Delta_2}} [/tex]
which is cannot follow. How do they know that the dependence is in the denominator and where does the exponent come from explicitely?
Any help is appreciated!
Thanks,
earth2
i'm studying Conformal Field Theory using the big yellow book by Senechal et al. So far everything has been a smooth ride. I'm a bit stuck at the point where they derive the 2- and 3-point correlator for spinless fields.
Based on invariance under rotations and translations the correlator should depend only on the relative coords of the quasi primary fields and moreover - because of scaling invariance - this dependence should be of the type
[tex] f(|x_1-x_2|)\sim \lambda^{\Delta_1+\Delta_2}f(\lambda|x_1-x_2|)[/tex] where λ is the scaling and Δ the conformal weight.
But then those guys say that this is nothing but
[tex]\langle \phi(x_1)\phi(x_2)\rangle \sim \frac{1}{|x_1-x_2|^{\Delta_1+\Delta_2}} [/tex]
which is cannot follow. How do they know that the dependence is in the denominator and where does the exponent come from explicitely?
Any help is appreciated!
Thanks,
earth2