Sunday, August 9, 2015

string theory - Why are the Nambu-Goto action and Polyakov action equivalent at quantum level?


It's a well known elementary fact that the Nambu-Goto action SNG=Tdτdσ(τXμ)2(σXμ)2(σXμτXμ)2 and Polyakov action SP=T2dτdσhhabημνaXμbXν are equivalent at the classical level. More precisely, by solving δSP/δhab=0 for hab and plugging it back to SP, we get SNG.


However, my question is whether they are equivalent at the quantum level or not. That is, if let ZP[J]:=D[hab]D[Xμ]exp(iSP[hab,Xμ]+idτdσJμXμ)D[hab]D[Xμ]exp(iSP[hab,Xμ]) and ZNG[J]:=D[Xμ]exp(iSNG[Xμ]+idτdσJμXμ)D[Xμ]exp(iSNG[Xμ]), do we also have ZP[J]=ZNG[J]?





No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...