Re: Non-commutative geometry

[Aiviet Nguyen <aiviet2@yahoo.com>]

Hi Tuan,

   I've had a look at that paper a mont ago and hardly
saw your conclusion. For me on contrary, the paper
revives the interest of NCG in physicist community:
now we should learn more NCG. Look at hep bulletin the
number of papers on NCG increases enormously recently.
   
   If you want to do M-theory I think definitely you
should know NCG ( no guarantee that would be enough,
as I saw some guys talking about non associative
geometry already :-))

   By the way, sometimes the Physicists mention NCG
but they don't mean
NCG a` la Connes.

   Non commutative spaces were discussed by a
physicist named Snyder
in his 1947 papers. Non commutative algebras of
space-time operators were discussed by Dirac even
earlier (between 20-30 or so).
  
   In Physics, Witten talked about NCG in 79-80.
Connes just introduced NCG to physcal contexts in late
80 or early 90.

   There are some differences in what they mean ( of
course they should have the smae foundation). However,
I think NCG term is used rather loosely by Witten and
Seiberg.

Cheers
Aiviet

--- "Tuan A. Tran" <tuan@feynman.physics.tamu.edu>
wrote: 
>  Recently, two American physicists Edward Witten va`
 Nathan Seiberg
> wrote a paper with 100 pages 
>  However, I was told as follows: 
> Seiberg and Witten showed that it is possible to map
non-commutative
> Yang-Mills fields to ordinary ones by a
transformation that maps one kind
> of gauge invariance to the other and adds higher
dimension terms to the
> equations of motion. So once you have a map, you
don't need to study
> non-commutative geometry.


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