The spectral action principle on Lorentzian scattering spaces

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.

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