Critcism, Zee's QFT, (KST)

On Jul 30, 9:56 pm, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:
"Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote in messagenews:1185838675.593386.210230@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx



On Jul 30, 3:33 pm, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:
Thanks Ken,

Goth "C" is first introduced by Zee in (I.3.18). He does not use it
much: "As a rule I will omit writing C altogether." But, it
"corresponds to the overall factor with the determinant in (I.3.16)"
and
in fact comprises an infinite product of these factors. Also, as Zee
notes at the end of Appendix A, "Various numerical factors have been
swept under the integration measure. In applying these formulas, be
certain that these factors are not relevant for your purposes."
These
factors are relevant for my purposes.

If there is nothing wrong with the line of development at:

http://jayryablon.files.wordpress.com/2007/07/quantization-update.pdf

then this can be turned into paper, with just some cleanup and a bit
more elaboration. To all: IS THERE ANYTHING AMISS IN THE NOTE AT THE
ABOVE LINK?

Yes there is IMHO, let's check Zee's (I.13.20) [sic -- you mean
I.3.20],

Jay, thank you for the correction.

specifically the term (x-y) therein, that's not
covariant. He didn't solve or explain that finite
difference, he just shucked it into a term, and
with simplifying notation, does that go away?

He goes further with that, see especially (I.3.22). The x-y turns into

exp[ik(x-y)] = exp[ikx] exp[-iky]

which in this form should be covariant. Yes? No? He also then Fourier
transforms this into momentum space. This is part of the propagator,
and I've never noticed a covariance problem with that.

I worry with Charles, some parts of QFT are
*smoke and mirror* mathematics, I've worked
that term, but do you (Jay) accept it?
Best regards
Ken S. Tucker
...

Well, I am trying to cut out the smoke and mirrors. I will tell you, I
think Zee is a superb reference. He cuts to the chase, focuses on
concepts rather than showing off by calculating everything under the
sun, and writes his book with enormous clarity, while almost daring the
reader to find ways to simplify and unify physics. It is the only
"simple" yet scientifically accurate book on QFT that exists today, and
it approaches a unification handbook, I believe, intentionally so.
Jay.

Jay, IMHO Zee's QFT is fundamentally flawed.
I'll explain, (hope the moderator's will allow this post).

Beginning with Zee's I.3.13 is a relativistic statement
vaguely connecting
frequency^2 = momentum^2 + mass^2 (Z.I.3.13)

(omega)^2 = k^2 + m^2.

Now the dimensionality is unclear, so I presumed
a few different ones, and settled on 1/time^2, in
the above.
( I recall Jay had a problem with that too).

Let me set the (x-y) in I.3.22 to "r" for
brevity. Then dr/dt maybe considered the invariant
*closure speed* of x relative to y, that's ok sofar.

Next same equation, the exponent on the RHS
has k*(x-y) == k*r == (dr/dt) * r = invariant.

Let's employ dr*r = dt*t where r =ct, then k*r
makes "t" invariant, but not "r", that's a logic bomb.

Going foward, Zee's I.5.6 please see the exponent
exp (-mr), which implies, (from above) the dimensionality
that m==1/t and r == t.

It's possible I/we might sort out that jungle by using
"c" as a variable in the spirit of GR, but it's cheaper
for me to take QFT from the ground up based on GR.

Best Regards
Ken S. Tucker

.

Quantcast