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Spin of the sress-energy tensor in d=2

  1. Mar 1, 2008 #1
    If we suggest a generic quantum field theory and assume that the theory is Poincare-Invariant (i.e. the corresponding Ward-Identities are satisfied) than the stress energy tensor in two dimensions can be written in terms of complex coordinates [tex]z,\bar{z}[/tex]as
    [tex]T^{zz}(z,\bar{z})=T^{00}-T^{11}-2iT^{10}[/tex]
    [tex]T^{\bar{z}\bar{z}}(z,\bar{z})=T^{00}-T^{11}+2iT^{10}[/tex]
    [tex]T^{z\bar{z}}(z,\bar{z})=T^{\bar{z}z}(z,\bar{z})=T^{00}+T^{11}\equiv -\Theta(z,\bar{z})[/tex]
    My question is how to find the Spin of the components [tex]T^{zz},T^{\bar{z}\bar{z}},\Theta[/tex]. The authors of the paper I'm studying claim
    [tex]ST^{zz}=2, ST^{\bar{z}\bar{z}}=-2 , S\Theta=0[/tex] but i don't see how . Can anyone help?
     
  2. jcsd
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