Re: Actions, Amplitudes, and the geometry of it all

Posted by DickT on October 02, 2003 at 15:48:10:

In Reply to: Re: Actions, Amplitudes, and the geometry of it all posted by Mike2 on October 02, 2003 at 12:11:25:

Mike,

I am going to try to develop something on the theme, From worldsheets to quantum amplitudes. I't try as hard as I can to keep it off the math, although I may have to introduce some tought concepts.

First installment. The interaction.

Strings interact by merging and separating. Restricting ourselves to closed strings, their worldsheets are tubes. Think of the "worldsheet of the interaction as a blob - like some sci fi monster - with the tubes of the interacting close strings coming into it and leaving it.

Where are the other ends of the tubes? Way, way off in the past or the furure. This is not a simple snapshot of nature at the string level, it's a Feynmann style combination of diagram and calculation framewrk. Some things, like the outside, are just left out.

Now one of the nice things about the Polykov action (the Weyl invariance part) allows us to continuously deform the tubes from long ago and the tubes to the far future into disc lying on the surface of the interaction blob. Draw a circle on the blob around the mouth where each tube joins it. Then map the time coordinate along the tubes (they are world tubes after all) into radial coordinates from the circle (which stays fixed) toward the center of the circle. The length along the radii becomes logarithmic so the arbitrary past and future corresponding to the center of the disc is never reached. It is a "punctured disc".

Next time: vertex operators.

Regards,
Dick

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Follow Ups: (Reload page to see most recent)

• Re: Actions, Amplitudes, and the geometry of it all -- Mike2 10/04/03 (1)
  • Re: Actions, Amplitudes, and the geometry of it all -- Mike2 10/10/03 (0)
• Vertex Operators -- DickT 10/04/03 (1)
  • Re: Vertex Operators -- Mike2 10/10/03 (0)
• Re: Actions, Amplitudes, and the geometry of it all -- Mike2 10/02/03 (0)

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