Ramanujan Summation and the Casimir Effect

Author: Wolfgang Bietenholz

Title: Ramanujan Summation and the Casimir Effect
Abstract:
This talk is dedicated to the memory of Srinivasa Ramanujan, the
self-taught Indian genius of mathematics, who died a century ago.
Among his achievements is a way to assign finite values to divergent
series, but he hardly left any explanation about it. Following the
few hints that he gave, we reconstruct a justification for his
approach, which provides correct values of the Riemann zeta function
with negative arguments. We further discuss physical application
of Ramanujan summation in the context of the Casimir effect, where
his way of removing a divergent constant corresponds to the
renormalization of the photon energy density. This leads to the
prediction of the Casimir force between conducting plates, which
has now been accurately confirmed by experiments.

Видео Ramanujan Summation and the Casimir Effect канала José Antonio GHz