Strange definition of regularization of Operators

[mhill]

surfing the web and arxiv i found the strange formula

$$lnA= \frac{d^{n}}{ds^{n}} \frac{s^{n-1}}{n! A^{s}}$$

my question is .. where does this formula come from ??

here 'n' is supposed to be a finite parameter we must define to avoid the divergences, is it valid for non-renormalizable or renormalizable theories ??

 

[ZapperZ]

surfing the web and arxiv i found the strange formula

Whenever you want to do something like this, you must make a full citation of the source to put this into a proper context. Or else this may not make any sense.

Zz.

 

[mhill]

oh excuse me Zapper i found it at http://books.google.es/books?id=PXk...tion&sig=zry2MSeyXNV0PbB4XqGFBB0BZvg#PPA76,M1

a preview of E. Elizalde's book page 75 and 76

 

[lbrits]

The $$-\lim_{s\to 0}$$ out in front is important.

 

[lbrits]

Formally taking a derivative wrt to $$A$$ on both sides should prove the identity to you.