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Science Forum Index » Physics - Research Forum » Question about Gaussian Intergal Underlying the "Central Identity of Quantum Field Theory"
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| Jay R. Yablon |
 Posted: Thu May 01, 2008 4:40 pm |
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I am trying to pinpoint the precise origins of the the term d/dJ which
appears as the argument in the potential V(d/dJ) in the so-called
"Central Identity of Quantum Field Theory," given on page 460 of Zee's
QFT in an Nutshell, and especially how one gets from V(x) --> V(d/dJ).
I have outlined my queries about this in a one page file linked below,
which also ties this query together with some of my other recent
queries:
http://jayryablon.files.wordpress.com/2008/04/central-identity.pdf .
Any help is appreciated. If clicking the link above does not work, then
right click and download the file, then open.
Thanks,
Jay.
____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm |
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| Posted: Sat May 03, 2008 7:59 pm |
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Jay R. Yablon wrote:
Quote: I am trying to pinpoint the precise origins of the the term d/dJ which
appears as the argument in the potential V(d/dJ) in the so-called
"Central Identity of Quantum Field Theory," given on page 460 of Zee's
QFT in an Nutshell, and especially how one gets from V(x) --> V(d/dJ).
Hey J-boy!
Isn't this done in Zee's "A baby problem" on pp42-43 ?
The steps leading up to formulas (3) and (4) ?
LOL with Neuropulp! |
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| Jay R. Yablon... |
| Posted: Sun May 04, 2008 10:30 am |
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<neuropulp at (no spam) yahoo.com.au> wrote in message
news:417d1152-4cf1-4648-ac8b-ddf20d4e621c at (no spam) 25g2000hsx.googlegroups.com...
Quote: Jay R. Yablon wrote:
I am trying to pinpoint the precise origins of the the term d/dJ
which
appears as the argument in the potential V(d/dJ) in the so-called
"Central Identity of Quantum Field Theory," given on page 460 of
Zee's
QFT in an Nutshell, and especially how one gets from V(x) --
V(d/dJ).
Hey J-boy!
Isn't this done in Zee's "A baby problem" on pp42-43 ?
The steps leading up to formulas (3) and (4) ?
LOL with Neuropulp!
Hey pulp-boy! ;-)
Yes it is. I was mulling though exactly that when I first made the
post, because I was looking for a good way to frame that derivation in
the most general way possible, and not be tied to that specific "baby
problem" in Zee. I think I have succeeded in that complete
generalization, which I have laid out in the ~1 page file linked below.
(If left click does not work, then right click to download, then open.)
http://jayryablon.files.wordpress.com/2008/05/zee-baby-problem.pdf
Does this pretty much answer the original question?
Thanks,
Jay. |
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| Jay R. Yablon... |
| Posted: Mon May 05, 2008 7:28 am |
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One other question:
The identity (6) at
http://jayryablon.files.wordpress.com/2008/05/zee-baby-problem.pdf is
based on B<>0 in (4). Does this dependence on non-zero B still apply to
(6)?
In other words: if B=0, then (6) transparently reduces to
($=integral -oo to +oo):
$exp[Ax^2-V(x)] = exp[-V(d/dB)] sqrt(2pi/A) (7)
But, what happens to the V(d/dB), since this only arises from (4) based
on assuming non-zero B. In (7), exp[-V(d/dB)] is only operating on
sqrt(2pi/A), with B=0. So, is (7) above a valid expression, and if so,
am I to conclude from taking a series expansion of exp[-V(d/dB)], then
having it operate on sqrt(2pi/A), that the whole expression
(7) = 0?
Thanks.
Jay. |
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