Re: Third Draft, Possible Closed Form Solution to Gaussian-Based Integrals with High-Order Field Interactions


"Dono" <sa_ge@xxxxxxxxxxx> wrote in message news:13558fdb-704b-4de0-a3ac-c91ca62bb766@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Nov 30, 9:55 am, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:
"Dono" <sa...@xxxxxxxxxxx> wrote in message

news:bcce17c7-87e8-4165-8bb5-2019c3e68ef6@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
. . .





> Jay,

> Basically you have two tasks in order to complete the proof:

> 1. Establish the conditions under which you can exchange the > Integral
> of the Derivative with the Derivative of the Integral (this is the
> "Theorem of Integrals Function of Parameter" I was refering to). In
> effect , you ned to prove the convergence of the integral before > you
> can exchange the order of integration and derivation.

> 2. Extend the "Theorem of Integrals Function of Parameter" to > include
> infinite series of functions. This one is going to be tougher, > unless
> you can find it in some book. The way it stands right now, you are
> applying the mechanisms without having a formal proof allowing you > to
> do so.

> PS: I emailed Eric what I thought might be wrong with his proof. > The
> residue computation is missing a singularity point at the infinity.

Thanks for bearing with me Dono.

Below I have posted a link to an excerpt from Zee's book where he
applies a very similar approach to what I have done here:

http://jayryablon.files.wordpress.com/2008/11/zee-baby-problem.pdf

What would be your comments about this use of "Theorem of Integrals
Function of Parameter"? Can you pinpoint how what he does is different
from what I do, if anything? Has he left something out? Is it implied?

In short, I don't see how what I am doing is really any different form
what he is doing -- in fact, all that is different is that I also have a
third-order term -- and I'd like to understand the difference, if any.

Jay.



Jay,

He's just as sloppy, he doesn't establish under what conditions the
order of integration and differentiation can be exchanged , i.e. he
doesn't establish the convergence of the integral BEFORE he puts it
through the mechanics.

I will make one other remark on all of this before moving on.

In a very basic sense, I am doing what everyone in this business does all the time when they cite references in papers. Even though they don't say it in this way, what they are really saying, with each and every citation used to support their position, is that "my ass is covered because this person before me who presumably knows what he or she is talking about did the same thing, and therefore, I don't have to repeat all the things that they went through that might have led them to what they did."

All I really did, was cite Zee. Period. But I did it in a more honest manner than is customary, because I came out and said "if it's good enough for Zee, it's good enough for me." Just what every physicist who writes papers with tons of citation is implicitly saying day in and day out, but without saying it in the candid way that I just did.

This is not, by the way, intended to be exculpatory. Quite the contrary, I fell prey to the same trap that many others also fall into, which was to lean on authority without always looking behind the authority. That is particularly anathema to someone like me, who believes that physics is in a terrible rut right now because most professionals who get the "time of day" are like lemmings, and most outsiders who are not like lemmings can't get the "time of day" from the insider lemmings. Physics these days is in need of fundamental change, and it will not come from the top down or the inside out, but from the bottom up and the outside in. Be assured of that.

That is one of the things that gives me a skewed impression of papers which cite zillions of references. What a reference is cited so that the reader can go back and be educated more deeply about a subject and thereby become a better reader, that is a worthy citation. When a reference is cited to say "he did it so I can do it," that is not a good citation, and that is the trap I fell into here.

Thanks for keeping me on my toes.

Jay.



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