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I am getting apparently conflicting statements about the conformal transformation law of the vertex operator appearing in and 2D QFT (such as in bosonic string theory). For example, according to http://en.wikipedia.org/wiki/Conformal_field_theory" [Broken] (eqn 64 on page 15), the transformation law is

where [itex]L_n[/itex] are the Virasoro generators and

which has

How do I reconcile this difference?

[tex][L_n,V(z)] = z^n\left(z\frac{d}{dz}+(n+1)h\right)V(z),[/tex]

where [itex]L_n[/itex] are the Virasoro generators and

*h*is the conformal weight of*V(z)*. But, according to Green, Schwarz, Witten's string theory book (Vol 1, eqn 7.1.3, p 356), the transformation law is[tex][L_n,V(z)] = z^n\left(z\frac{d}{dz}+nh\right)V(z),[/tex]

which has

*n*instead of (*n*+1). These two equations describe pretty different transformation properties, and I don't know who to believe. The first one makes more sense, but when I actually try to derive the transformation law, I find the get the second one.How do I reconcile this difference?

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