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**What is Spectral Geometry ??**

in many cases of Connes' work he introduced the concept (??) of spectral geometry, replacing the derivatives by commutators so

[tex] df \rightarrow (f,A) [/tex] what does 'A' here mean ?? , it is similar to the Heisenberg

equation of motion ?? [tex] \dot f = (f,H) [/tex]

Also instead of integrals he used expressions like

[tex] \int T = Res_{s=0} Tr( f|D|^{-s}) [/tex]

also he defined an 'infinitesimal operator' (??) [tex] dx [/tex] or integral of infinitesimal operator as the value of the log(e) inside [tex] Tr_{e}[/tex] or something similar.

the .pdf bear the name ' NONCOMMUTATIVE GEOMETRY AND PHYSICS' by the Physicist Alain Connes, i have tried googling but the papers that appeared had a heavy content on algebra and Galois theory.