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In my Book (Becker, Becker, Schwarz) it is stated (eq 3.23) that the holomorphic component of the EM tensor is given by

[tex]T_X(z)=T_{zz}=-2 : \partial _z X \cdot \partial _z X :[/tex]

Now why is the expression for the (holonorphic, zz, component of the) energy momentum tensor in complex coordinates?

[tex]T_X(z)=T_{zz}=-2 : \partial _z X \cdot \partial _z X :[/tex]

Now why is the expression for the (holonorphic, zz, component of the) energy momentum tensor in complex coordinates?

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