Re: Closed Strings, World-sheets, and Stoke's Theorem

Posted by DickT on September 29, 2003 at 11:27:01:

In Reply to: Closed Strings, World-sheets, and Stoke's Theorem posted by Mike2 on September 29, 2003 at 07:15:08:

Mike,

Polichinski, after motivating with a discussion of point particles (the simplest action is proportional to the proper time on the particle's worldline), introduces the Nambu-Goto action for the bosonic string, proportional to the area of the worldsheet. "As in the case of the particle, we insist that physical quantities such as the action depend only on the embedding [of the sheet] in spacetime and not on the parametrization."

Because the Nambu-Goto action has derivatives under the square root sign, it is hard to work with. So a number of physicists (Brink, Di Vecchia, & Howe, and Deser & Zumino in the supersymmetry context), and Polyakov in the string context, introduced the Polyakov action. This is equivalent to the NG action but is expressed in terms of an independent worldsheet metric.

The Polyakov action is invariant unde D-dimensional Poincare, diffeomeorpisms, and Weyl invariance on the worldsheet. All of these invariances play a big part in developing the theory.

Regards,
Dick

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Follow Ups: (Reload page to see most recent)

• Re: Closed Strings, World-sheets, and Stoke's Theorem -- Mike2 9/29/03 (4)
  • Re: Closed Strings, World-sheets, and Stoke's Theorem -- DickT 9/30/03 (3)
    • Re: Closed Strings, World-sheets, and Stoke's Theorem -- Mike2 9/30/03 (2)
      • Re: Closed Strings, World-sheets, and Stoke's Theorem -- DickT 9/30/03 (1)
        • Re: Closed Strings, World-sheets, and Stoke's Theorem -- Mike2 9/30/03 (0)

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