Sunday, January 30, 2011

Motives, Twistors and Amplitudes

Nima Arkani-Hamed gave a recent talk on 01/26 entitled "Space-Time, Quantum Mechanics and Scattering Amplitudes". He essentially covers all the recent progress in the study of scattering amplitudes in dual twistor variables. He ends with hints at an underlying theory that gives rise to AdS/CFT and QFT, which might be based on the mathematical theory of motives.

For those unfamiliar the theory of motives, the goal within the mathematical community is to define a unified cohomology theory, from which all others (de Rham, Čech, singular, etc.) are special cases. It is interesting that a unified theory of physics would coincide with this platonic goal of mathematicians. Perhaps Edward Witten foresaw such a convergence and the 'M' of M-theory stood for motive all along. Either way, category theorists saw this coming a few years ago.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

— Albert Einstein