Dilogarithm Motives in Physics

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About this episode

Spencer Bloch

"Dilogarithm Motives Arising in Physics"

Talk given at "Algebraic Geometry, K-theory, and Motives" (a conference dedicated to Andrei Suslin's 60th birthday) St. Petersburg, Russia June 25-29, 2010.

In this very clear talk, Bloch explains how one is often writing down interesting periods on n-dimensional projective space when doing high energy physics. One can start with a hypersurface defined by the vanishing of a certain configuration polynomial F of degree d. F determines the hypersurface X, and X determines the motive.

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