nLab
motivic multiple zeta values

Context

Motivic cohomology

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

Where a zeta function and multiple zeta function may be assigned to a suitable variety, so a motivic multiple zeta function is attached to the corresponding motive, like a motivic L-function is.

Where zeta functions appear in physics as expressions for vacuum amplitudes, so multiple zeta functions appear in expressions for more general scattering amplitudes. The intricate combinatorics of these becomes often more tractable when re-expressing them as motivic multiple zeta values (e.g. Schlotterer-Stieberger 12).

References

General

  • Francis Brown, On the decomposition of motivic multiple zeta values (arXiv:1102.1310v2)

  • A. B. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry (arXiv:math/0208144)

In physics (scattering amplitudes)

In scattering amplitudes.

Of the superstring:

In N=4 D=4 super Yang-Mills theory:

  • Marcus Spradlin, Anastasia Volovich, Symbols of One-Loop Integrals From Mixed Tate Motives (arXiv:1105.2024)

See also at motives in physics.

Revised on September 11, 2014 06:15:52 by Urs Schreiber (185.26.182.31)