Re: Renormalization

From: Igor Khavkine (igor.kh_at_gmail.com)
Date: 03/30/05


Date: Wed, 30 Mar 2005 00:40:26 +0000 (UTC)

On 2005-03-24, Eugene Stefanovich <eugenev@synopsys.com> wrote:
> Igor Khavkine wrote:
>> On Tue, 22 Mar 2005 08:18:53 +0000, Eugene Stefanovich wrote:
>>
>>>Igor Khavkine wrote:

Regarding finite time calculations:

>>>>The procedure is the same as for standard perturbation theory however,
>>>>the upper limit on the time integrals is kept finite instead of
>>>>infinite.

[...]

> I fail to see how your 8-step procedure is going to work when at each
> step you face infinite linear combinations whose coefficients
> are infinite (in the limit of infinite cutoff). I am sure that these
> infinities would not cancel when you come to step 8.

Have you tried it? Otherwise you should not be so quick to dismiss it.
I don't have time to do this calculation myself. But, if you are
willing, I can tell you exactly what to do.

Igor



Relevant Pages

  • Question on definition of transcendental numbers
    ... finite number of coefficients. ... For instance, Pi is transcendental over Q, however by the usual taylor ... general constructions for any transcendental number, ... easier non-constructive way to see the existence of such an infinite ...
    (sci.math)
  • Re: Question on definition of transcendental numbers
    ... such that there does not exist a polynomial, with rational (equiv. ... finite number of coefficients. ... general constructions for any transcendental number, ... easier non-constructive way to see the existence of such an infinite ...
    (sci.math)
  • Re: Infinite-Precision Dgital Filters
    ... They seem to refer to coefficients represented with floating ... "The infinite-precision filter, h, is generated by the ... are they refering to infinite precision of the DATA or infinite ... precision of the COEFFICIENTS of the filter? ...
    (comp.dsp)
  • Re: Interpolation using polyphase FIR filter: Finding coeffisients
    ... I thought duplicating the nearest sample would give unwanted repeating ... duplicating samples will create spectral aliasing. ... number of coefficients, without bound. ... If you don't want an infinite ...
    (comp.dsp)
  • Re: infinity
    ... I was thinking that the polynomials' coefficient sequences would map to ... We want to represent the integer coefficients of all polynomials. ... We have that Z^n is an infinite set and a countably infinite set. ...
    (sci.math)