# The spectral action principle on Lorentzian scattering spaces

## Location

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.