Friday, February 26, 2021 11:00 AM
Dang Nguyen Viet (Université Claude Bernard Lyon 1)

Abstract: This is joint work with Michal Wrochna. 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. When \$d=4\$, we show the pole
at \$s=1\$ equals a generalized Wodzicki residue and is proportional to
the Einstein-Hilbert action density, proving a spectral action
principle in Lorentz signature.