The spectral action principle on Lorentzian scattering spaces

07.05.2021, 11:00  –  Online Seminar
Arbeitsgruppenseminar Analysis

Viet Dang (University of Lyon)

The spectral action principle of Connes recovers the Einstein Hilbert action from spectral data and is one of the cornerstones of the noncommutative geometry approach to the standard model, yet it is limited to compact Riemannian manifolds which is incompatible with General Relativity. Generalizing the principle to the Lorentz signature has been a longstanding open problem. In the present work, we give a global definition of complex Feynman powers $(\square+m^{^2}+i0)^{-s}$ on Lorentzian scattering spaces, and show that the restriction of their Schwartz kernel to the diagonal has a meromorphic continuation. We also give a new dynamical definition of Wodzicki residue and generalize it to certain negative powers of the Feynman inverse. In even dimension, we show the pole at $s=d/2-1$ equals the generalized Wodzicki residue and is proportional to the Einstein-Hilbert action density, proving a spectral action principle in Lorentz signature. This is joint work with Michal Wrochna.

Forthcoming speakers are Yannic Vargas on May 14th, John Barrett  on May 21st, Malte Leimbach on May 28th, Alfonso Garmendia on June 4th, Konrad Waldorf on June 11th and Bernadette Lessel on July 2nd.

You are welcome to invite your friends and colleagues to join us! If you wish to attend the talks,  please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.