# Weil positivity and trace formula the archimedean place

@article{Connes2020WeilPA, title={Weil positivity and trace formula the archimedean place}, author={Alain Connes and Caterina Consani}, journal={Selecta Mathematica}, year={2020}, volume={27}, pages={1-70} }

We provide a potential conceptual reason for the positivity of the Weil functional using the Hilbert space framework of the semi-local trace formula of Connes (Sel Math (NS) 5(1):29–106, 1999). We explore in great details the simplest case of the single archimedean place. The root of this result is the positivity of the trace of the scaling action compressed onto the orthogonal complement of the range of the cutoff projections associated to the cutoff in phase space, for $$\Lambda =1$$ Λ = 1…

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