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Jay R. Yablon
Nov4-06, 03:38 PM
P: n/a
"Igor Khavkine" <> wrote in message
.. . .
>> > Also, gravity is more than just a metric tensor. It is the metric
>> > tensor coupled to matter in a specific way. For instance, in a
>> > Lagrangian density with some scalar and and spinor fields, it
>> > enters
>> > as
>> > follows (G - metric, @ - partial derivative, g - gamma matrix, A -
>> > vector potential):
>> >
>> > magnetic moment correction --+
>> > v
>> > L = G @phi @phi + psi g @psi + psi (g + lambda) A psi + ...
>> > ^ ^ ^
>> > |__ gravity |__ gravity |__ gravity
>> >
>> > When writing down the effective action (which is the only place
>> > where the corrected vertex factor you refer to actually makes an
>> > appearance), each coefficient shown above changes in a particular
>> > way compared to its bare value. The G, g (in the psi-psi term), and
>> > g (in the psi-A-psi) term will all change according to different
>> > rules. There is no reason to expect them to conspire to change such
>> > that G stays equal to the anticommutators of the g+lambda
>> > components.
>> >
>> > Igor
>> >

.. . .
> The answer to the your new question is already present in my previous
> reply. To help you decode it, I will place emphasis on the key words
> that may have obscured its meaning.
>> > ... [different terms of] the effective action ... will all change
>> > according to different rules ... compared to [their] bare values.

> So, what is an "effective action"? And how do the terms in the
> effective action change compared to their bare value?
> Finally, the actual answer to your question is negative. Again,
> *generically* there is no reason for any of the coefficients of the
> effective action to change in unison with the coefficient of
> fermion-photon coupling. In fact, the same kind of coefficient will
> not
> change in the same way between different fermions, as evidenced by
> say different magnetic moments of different elementary particles.
> Igor

Thank you again for your reply Igor. I also want to take a moment to
thank you for what I have come to see as a real service to people who
are doing physics study and research in providing the feedback and
critiques that you do. For those of us who try as best as we can to
keep our ears open and understand your input, it is very helpful. And
since it is probably thankless for you most of the time, I do want to
again say thank you.

Before proceeding further, I want to make certain I am absolutely clear
about what you are saying:

I understand you to say that just because the "effective action" based
on "psi (g + lambda) A psi" for the "fermion-photon coupling" is
perturbatively corrected from its "bare value" "psi g A psi," there is
no reason to expect that the "bare" term "psi g @psi" will similarly
become "corrected" to "psi (g + lambda) @psi," or that the "bare" metric
tensor G=.5{g,g} will become "corrected" to G=.5{g + lambda,g +
lambda}. Is this an accurate restatement?

I also understand you to say in your final sentence that the "different
magnetic moments of different elementary particles" are understood
*because* one does *not* change all of these coefficients in unison and
that were these to change in unison, we would not be able to explain why
different elementary particles have different magnetic moments. In sum,
you seem to me to say that the "different magnetic moments of different
elementary particles" are evidence that these coefficients do not /
cannot change in unison, because if they did change in unison, then
these fermions would all have the *same* magnetic moment. Is that
accurate? (I will note that in a separate post, I did ask about how the
differences among the electron, mu and tau lepton magnetic moments are
presently accounted for, but nobody has replied to that. I am still
interested in hearing about this, because my impression, studying Ryder,
is that this is a problem not fully-understood at present and I would
like to know what the "best" understanding is.)

Finally, when you refer to "different magnetic moments of different
elementary particles," I take it that you are thinking, in particular,
of the electron, mu and tau leptons, and the fifth-digit variations in
magnetic moments among these three particles. Is that also accurate?


Jay R. Yablon
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