Résumé : This is joint work with Michal Wrochna. The spectral action principle of Connes is one of the cornerstones of the noncommutative geometry approach to the standard model, yet it is limited to the setting of 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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