Urs tutorial on Connes spectral geometry

[rtharbaugh1]

Now I imagine that g is something like a simplex, only perhaps with a dimension along the possible worldlines included. Is this the idea?

I am going to listen to Connes as Marcus suggested in an earlier post, as I have now temporary access to a broadband bubble.

R.

Seems I can't understand the talk...maybe accent problem, or microphone, or my inability to recognise the concept vocabulary.

Oh well. Back to reading.

R

 

[mhill]

the idea is , if you drop commutativity of the derivative and similar then you define

the 'derivative' of f respect to 'x' as $$\frac{df}{dx}= [f, A]$$

but the question is what is 'A' operator ??

and for the 'integral' how can you define or justify this

$$\int f |D| = Res_{s=0} Tr( f |D|^{-s} )$$

and it would be so simple as this ? you would replace the 'normal' derivative and integral by taking a Trace or commutators ??