Abstract
In the last couple of years there has been a growing interest in two dimensional field theories possessing conformal symmetry for their applications to two dimensional statistical systems at critical points)-7) and to (super)string theories. l) Of paramount importance in such theories is the role played by the energy momentum tensor. Infinitesimal conformal transformations are generated by the energy momentum tensor and the infinitesimal transformation law of the energy momentum tensor itself is equivalent to the algebra of conformal invariance, i.e., the Virasoro algebra. There is a natural question one can raise: How does the energy momentum tensor transform under not an infinitesimal but a finite conformal transformation? In the seminal paper of Belavin, Polyakov and Zamolodchikov,l) it has been noted that under a finite conformal change of coordinates z-> w=u(z) the energy momentum tensor Tzz(z) should transform as:
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