Re: non-integer dimensions of physical or non-physical quantities

Posted by DickT on October 08, 2003 at 13:02:47:

In Reply to: non-integer dimensions of physical or non-physical quantities posted by ceco on October 08, 2003 at 08:42:44:

Ceco,

In Quantum Field Theory there is dimensional regularization, but I am pretty sure no-one thinks of it as invoking actual non-integral dimensions. The method (introduced by Veltzmann and t'Hooft who won the Nobel Prize for it) works an the basis that field theory is finite in 2 dimensions. The problem they want to solve is the untra violet infinity in 4-dimensional field theory. So they create a continuum of dimesions between 4 and 2 with a theory for each one; this is all formal, at the notation level. From this connection between finite theory and infinte theory they derive a modification (a regulator) to the 4 dimensional theory which renders it free of the ultra violet divergence. Later the regulator will be subsumed into a measured value. This is renormalzation.

Regards,
Dick

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