On Wed, Jul 02, 2003 at 08:05:00PM -0400, asimovd@aol.com wrote:
Overbye mentions that string theory has made the subject of Riemann surfaces a hot topic. Can anyone please explain this remark to me? (Please bear in mind that I have only a vague metaphoric idea of what string theory is about.)
(First guess: String theory as I understand it posits little simple closed curves in physics space (11 dimensional?) a what underlie elementary particles. Maybe now someone has suggested replacing the s.c.c.'s with surfaces?)
Not quite. String theory posits replacing particles with little curves, but then when the curves propogate you add an extra time dimension, getting surfaces. The resulting theory is nearly conformally invariant[1], so you end up studying Riemann surfaces. Usually physicists are happy doing calculations with (perforated) spheres and tori, but for higher-order corrections you need to understand the moduli of Riemann surfaces better. Peace, Dylan [1] One might well ask why the metric on the surface is Euclidean rather than Lorentzian. I think you do some sort of analytic continuation.