Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Weyl Transformation and Scalar Product

  1. Jul 1, 2004 #1
    I was reading about Weyl Transformations in Polchinski's book and I have a little doubt: Is it correct to say that under a Weyl transformation the scalars are invariant, i.e., that a weyl transformation preserves the scalar product?
  2. jcsd
  3. Jul 1, 2004 #2


    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Hmm, the Weyl transformation says that if you multiply the metric tensor [tex]\gamma_{(\tau,\sigma)}[/tex] on the world sheet by the exponential of an arbitrary world sheet function, while keeping the X potentials the same, the metric doesn't change. Basically the transformed metric defines the same spacetime embedding as the original, WT being a degree of freedom in the derivation of the Polyakov action from the Nambu-Goto action. So I would say, yes, the scalar product is preserved by WT, and so are all the other tensor operations on the world sheet.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook