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Lorentz violation of the Standard Model
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Igor Khavkine



Joined: 05 Aug 2006
Posts: 21

PostPosted: Mon Oct 16, 2006 1:56 pm    Post subject: Re: Lorentz violation of the Standard Model Reply with quote

Subject: Re: Lorentz violation of the Standard Model
From: "Igor Khavkine" <igor.kh@gmail.com>
Date: Mon, 24 Apr 2006 21:28:40 +0000 (UTC)
Approved: helbig@astro.mNuOlStPiAvMax.de (sci.physics.research) X-Mod-No.: 07
Message-ID: <1145746511.056590.14350@j33g2000cwa.googlegroups.com>
Newsgroups: sci.physics.research
Organization: http://groups.google.com
References: <dvlna4$egh$1@gnus01.u.washington.edu>


J.C. Yoon wrote:

> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> slrne48t39.dde.igor.kh@corum.multiverse.ca">news:slrne48t39.dde.igor.kh@corum.multiverse.ca...
> > What you show below is an attempt to find wave function solutions to
> > the Dirac equation. Since you and Weinberg are talking about different
> > mathematical objects, there will be little if anything at all that can
> > be compared in your respective conclusions.
>
> Do you claim that the fields of the SM different from
> the wave function solutions to the Dirac equations,
> but the results of its calculations are the same?

Yes, I've pointed out the difference between quantum fields and wave
functions several times in this thread. What calculation do you mean?
One does different calculations with wave functions than with fields.
If the computed quantities are in principle different, then it makes
little sense to ask wether they are the same. The difference between
wave functions and quantum fields is well explained in the last chapter
of Weinberg's first volume on QFT.

> > ...
> > If you choose to start the p.t. calculation from massless fields
> > (including the mass as an interaction), there will be other steps that
> > are not present in the simpler calculation given in Chapter 5 of P&S.
> > However, the resulting formula for the total cross section will be the
> > same as as in (5.13).
>
> According to your account, QED calculation with
> massive fermion P&S (5.13) will be the same as the
> SM calculation with massless fermion with infinite
> diagrams.

Why do you compare QED and the SM? These are two different field
theories. My comments apply to QFT's in general. Fix a QFT (be it QED
or the standard model), then p.t. calculations in this theory can be
done in more than one way, as I've explained in previous posts. Once
you grasp this point, you can apply it to any field theory that you
want.

> However, SLAC E158 claims that not the
> exact QED calculation like P&S (5.13), but the
> approximated one like P&S (5.14) should be the SM
> calculation.

I'm sorry, this sentence is hard for me to understand. The only
difference between P&S's (5.13) and (5.14) is that, in the latter, one
expands in powers of the ratio of muon's mass to its energy in the
center of mass frame. Once the cross section in (5.13) is obtained, the
last step is trivial. The only requirement for its applicability is
that the above ratio is small.

> Do you claim that SLAC E158 fails to calculate the
> SM prediction properly?

I have no reason to suspect that the SLAC team made a mistake in their
calculations. And none of what I said in this thread contradicts their
results.

Igor
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jcyoon



Joined: 08 Aug 2006
Posts: 213

PostPosted: Mon Oct 16, 2006 1:58 pm    Post subject: Re: Lorentz violation of the Standard Model Reply with quote

Subject: Re: Lorentz violation of the Standard Model
From: "J.C. Yoon" <jcyoon@u.washington.edu>
Date: Fri, 28 Apr 2006 04:35:48 +0000 (UTC)
Approved: igor.kh@gmail.com (sci.physics.research)
Message-ID: <e2ohlr$80a$1@gnus01.u.washington.edu>
Newsgroups: sci.physics.research
Organization: University of Washington
References: <dvlna4$egh$1@gnus01.u.washington.edu><1145746511.056590.14350@j33g2000cwa.googlegroups.com>
Sender: igor@bigbang.richmond.edu

Dear Igor Khavkine,

Thanks for you reply and answers to my questions.

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
1145746511.056590.14350@j33g2000cwa.googlegroups.com">news:1145746511.056590.14350@j33g2000cwa.googlegroups.com...
>
> Yes, I've pointed out the difference between quantum fields and wave
> functions several times in this thread. What calculation do you mean?
> One does different calculations with wave functions than with fields.
> If the computed quantities are in principle different, then it makes
> little sense to ask wether they are the same. The difference between
> wave functions and quantum fields is well explained in the last
chapter
> of Weinberg's first volume on QFT.
>
> Why do you compare QED and the SM? These are two different field
> theories. My comments apply to QFT's in general. Fix a QFT (be it QED
> or the standard model), then p.t. calculations in this theory can be
> done in more than one way, as I've explained in previous posts. Once
> you grasp this point, you can apply it to any field theory that you
> want.
>
> I'm sorry, this sentence is hard for me to understand. The only
> difference between P&S's (5.13) and (5.14) is that, in the latter, one
> expands in powers of the ratio of muon's mass to its energy in the
> center of mass frame. Once the cross section in (5.13) is obtained,
the
> last step is trivial. The only requirement for its applicability is
> that the above ratio is small.

I meant the calculations that you mentioned; the total cross
section of electron and muon from QED such as P&S (5.13)
and the one from QFT and the SM calculation.

I am trying to compare QED and the SM since you claimed
that the total cross section calculation from QED and the SM
is the same as in P&S (5.13) and the high-energy
approximation can be applied to both QED and the SM
so that we have P&S (5.14).

Is it what you meant to say?

Thanks,
J.C. Yoon
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Igor Khavkine



Joined: 05 Aug 2006
Posts: 21

PostPosted: Mon Oct 16, 2006 1:59 pm    Post subject: Re: Lorentz violation of the Standard Model Reply with quote

Subject: Re: Lorentz violation of the Standard Model
From: "Igor Khavkine" <igor.kh@gmail.com>
Date: Sat, 29 Apr 2006 06:44:05 +0000 (UTC)
Approved: helbig@astro.mNuOlStPiAvMax.de (sci.physics.research) X-Mod-No.: 05
Message-ID: <1146204572.313462.154580@i40g2000cwc.googlegroups.com>
Newsgroups: sci.physics.research
Organization: http://groups.google.com
References: <dvlna4$egh$1@gnus01.u.washington.edu>


J.C. Yoon wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> 1145746511.056590.14350@j33g2000cwa.googlegroups.com">news:1145746511.056590.14350@j33g2000cwa.googlegroups.com...

> > Why do you compare QED and the SM? These are two different field
> > theories. My comments apply to QFT's in general. Fix a QFT (be it
> > QED or the standard model), then p.t. calculations in this theory
> > can be done in more than one way, as I've explained in previous
> > posts. Once you grasp this point, you can apply it to any field
> > theory that you want.
[...]
> > I'm sorry, this sentence is hard for me to understand. The only
> > difference between P&S's (5.13) and (5.14) is that, in the latter,
> > one expands in powers of the ratio of muon's mass to its energy in
> > the center of mass frame. Once the cross section in (5.13) is
> > obtained, the last step is trivial. The only requirement for its
> > applicability is that the above ratio is small.
>
> I meant the calculations that you mentioned; the total cross section
> of electron and muon from QED such as P&S (5.13) and the one from
> QFT and the SM calculation.

Let me make more clear the point I made in the top paragraph above. The
comments that I've been making about perturbation theory are applicable
to any quantum field theory (QFT). Both QED and the SM are QFT's,
therefore you can take either massive or massless bare particles as a
foundation for perturbation theory in both QED and the SM. In other
words, each possibility given in the following table is possible:

\ QFT| | |
bare \ | | Standard |
particles \ | QED | Model |
in p.t. \ | | |
--------------+-------+----------+
massive | Yes | Yes* |
--------------+-------+----------+
massless | Yes | Yes |
--------------+-------+----------+

* There is a caveat here. As Hendrik van Hees already pointed out,
introducing mass terms directly into the SM Lagrantian spoils
some symmetries and renormalizability. But it is perfectly possible
to do so after Higgs symmetry breaking has taken place.

Each cell in the above table gives you a way to set up perterbative
calculations in the given QFT. If you fix the QFT, then the cross
section for e+e- -> mu+mu- scattering is a physical result and is
independent of the method of calculation. Therefore, a calculation of
this cross section will yield the same result in each cell of the QED
column, and similarly for the SM column. However, there will be a
slight difference between the results in different columns. Simply put,
the SM contains more kinds of interactions, hence the cross section is
expected to differ between the two theories.

> I am trying to compare QED and the SM since you claimed that the
> total cross section calculation from QED and the SM is the same as in
> P&S (5.13) and the high-energy approximation can be applied to both
> QED and the SM so that we have P&S (5.14).

There is nothing deep or mysterious about the high (center of mass)
energy expansion. One writes down the formula for a cross section.
Then, if it can be expressed as a function of m/E, where m is a mass
and E is the center of mass energy, then one can expand this formula in
m/E and claim that the first few terms are a good approximation when
m << E. Taylor's theorem is oblivious which field theory you are using.

> Is it what you meant to say?

P&S do the calculation that would correspond to the (massive,QED) cell
in the above table. What I'm trying to tell you is that the same
calculation can be done corresponding to the (massless,QED) cell and
yield the same answer as (5.13), from which (5.14) follows by
elementary Taylor expansion.

P&S do not do the equivalent calculation with the SM (simply because it
is more complicated and involves many more Feynman diagrams). But, in
principle, both the (massive,SM) and (massless,SM) calculations are
possible and will yield the same physical results.

Instead of idly wondering what may or may not be possible, I highly
recommend that you actually sit down and perform the (massless,QED)
calculation. You mentioned previously that you weren't sure how to do
it. But you also never answered my questions about your level of
familiarity with standard QFT tools. So, once more. Have you tried this
calculation? If not, you should. If yes, then what was your difficulty?

Igor
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jcyoon



Joined: 08 Aug 2006
Posts: 213

PostPosted: Mon Oct 16, 2006 2:00 pm    Post subject: Re: Lorentz violation of the Standard Model Reply with quote

Subject: Re: Lorentz violation of the Standard Model
From: "J.C. Yoon" <jcyoon@u.washington.edu>
Date: Wed, 3 May 2006 00:52:44 +0000 (UTC)
Approved: igor.kh@gmail.com (sci.physics.research)
Message-ID: <e359ms$31l$1@gnus01.u.washington.edu>
Newsgroups: sci.physics.research
Organization: University of Washington
References: <dvlna4$egh$1@gnus01.u.washington.edu><1146204572.313462.154580@i40g2000cwc.googlegroups.com>
Sender: igor@bigbang.richmond.edu

Dear Igor Khavkine,

Thanks for elaborating your comments.
As you recommend I would like to perform the SM
calculations, but I need to make sure a couple
more things.

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:1146204572.313462.154580@i40g2000cwc.googlegroups.com...
>...
> However, there will be a slight difference between the results in
> different columns. Simply put, the SM contains more kinds of
> interactions, hence the cross section is expected to differ between
> the two theories. ... P&S do not do the equivalent calculation with
> the SM (simply because it is more complicated and involves many more
> Feynman diagrams). But, in principle, both the (massive,SM) and
> (massless,SM) calculations are possible and will yield the same
> physical results.
>

"Igor Khavkine" wrote
>If you choose to start the p.t. calculation from massless fields
>(including the mass as an interaction), there will be other steps that
>are not present in the simpler calculation given in Chapter 5 of P&S.
>However, the resulting formula for the total cross section will be the
>same as as in (5.13).

I am confused here. In previous posts you said you can
get P&S result (5.13) from the SM calculation starting with
massless and mass interaction. But here you say it could
be different at some point.

Could you make sure whether the result (5.13) is exactly
the same or not? If not, please let me know the exact result
so that I can follow your calculation.

Thanks,
J.C. Yoon
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Igor Khavkine



Joined: 05 Aug 2006
Posts: 21

PostPosted: Mon Oct 16, 2006 2:01 pm    Post subject: Re: Lorentz violation of the Standard Model Reply with quote

Subject: Re: Lorentz violation of the Standard Model
From: Igor Khavkine <igor.kh@gmail.com>
Date: Thu, 4 May 2006 05:11:46 +0000 (UTC)
Approved: igor.kh@gmail.com (sci.physics.research)
Message-ID: <slrne5g521.tkd.igor.kh@corum.multiverse.ca>
Newsgroups: sci.physics.research
Organization: University of Western Ontario
References: <dvlna4$egh$1@gnus01.u.washington.edu><1146204572.313462.154580@i40g2000cwc.googlegroups.com><e359ms$31l$1@gnus01.u.washington.edu>
Sender: igor@bigbang.richmond.edu
User-Agent: slrn/0.9.8.1pl1 (Debian)


On 2006-05-03, J.C. Yoon <jcyoon@u.washington.edu> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:1146204572.313462.154580@i40g2000cwc.googlegroups.com...
>>...
>> However, there will be a slight difference between the results in
>> different columns. Simply put, the SM contains more kinds of
>> interactions, hence the cross section is expected to differ between
>> the two theories. ... P&S do not do the equivalent calculation with
>> the SM (simply because it is more complicated and involves many more
>> Feynman diagrams). But, in principle, both the (massive,SM) and
>> (massless,SM) calculations are possible and will yield the same
>> physical results.

Just to clarify, again, (massless,SM) will give the same result as
(massive,SM), while (massless,QED) will give the same result as
(massive,QED). On the other hand, the results of (massles/massive,SM)
will be different from (massless/massive,QED), simply because SM and QED
are different field theories.

>
> "Igor Khavkine" wrote
>> If you choose to start the p.t. calculation from massless fields
>> (including the mass as an interaction), there will be other steps that
>> are not present in the simpler calculation given in Chapter 5 of P&S.
>> However, the resulting formula for the total cross section will be the
>> same as as in (5.13).
>
> I am confused here. In previous posts you said you can
> get P&S result (5.13) from the SM calculation starting with
> massless and mass interaction. But here you say it could
> be different at some point.

You are confused because that's not what I said. First, I suggest you
forget about the standard model (for now) and don't come back to it
until you have a better understanding of QFT calculation techniques.

QED and SM are two different quantum field theories. QED contains
Dirac (e.g. electrons and muons) fermion onand Maxwell fields. SM is a
superset of QED. In addition, it also contains quarks, W and Z bosons,
as well as gluons. Obviously QED is simpler to deal with, that's why
it's used for introductory examples in P&S instead of the full blow SM.

> Could you make sure whether the result (5.13) is exactly
> the same or not? If not, please let me know the exact result
> so that I can follow your calculation.

P&S's (5.13) is the result of a QED calculation. What do you want to
compare it to? What I've been explaining in this thread is the
possibility of choosing different bare Hamiltonians to do perturbation
theory. This can be done in *any* QFT (which includes QED). If you are
still wondering, whether there are two distinct QED calculations that
can yield the result (5.13), the answer is still Yes.

Again, my advice to you is to forget about the standard model and deal
with a simpler theory like QED. If you want to treat the mass terms of
QED as interactions (i.e. start with a massless bare Hamiltonian), you
have to be familiar with a few QFT methods. As I mentioned previously,
these include (1) bare propagators, (2) self-energy calculation, (3)
Dyson's formula, (4) renormalized propagators, (5) LSZ reduction
formula. You still haven't said whether you are familiar with any of
these. If you are not, you have to learn about them and how to use them
before you can do this kind of calculation.

Igor
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jcyoon



Joined: 08 Aug 2006
Posts: 213

PostPosted: Mon Oct 16, 2006 2:02 pm    Post subject: Re: Lorentz violation of the Standard Model Reply with quote

Subject: Re: Lorentz violation of the Standard Model
From: "J.C. Yoon" <jcyoon@u.washington.edu>
Date: Thu, 11 May 2006 23:02:47 +0000 (UTC)
Approved: igor.kh@gmail.com (sci.physics.research)
Message-ID: <e3vl67$3hm$1@gnus01.u.washington.edu>
Newsgroups: sci.physics.research
Organization: University of Washington
References: <dvlna4$egh$1@gnus01.u.washington.edu><1146204572.313462.154580@i40g2000cwc.googlegroups.com>
<e359ms$31l$1@gnus01.u.washington.edu><slrne5g521.tkd.igor.kh@corum.multiverse.ca>
Sender: igor@bigbang.richmond.edu


Dear Igor Khavkine,

Thank your for the clarification.

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
slrne5g521.tkd.igor.kh@corum.multiverse.ca">news:slrne5g521.tkd.igor.kh@corum.multiverse.ca...
>
> Again, my advice to you is to forget about the standard model and deal
> with a simpler theory like QED. If you want to treat the mass terms of
> QED as interactions (i.e. start with a massless bare Hamiltonian), you
> have to be familiar with a few QFT methods. As I mentioned previously,
> these include (1) bare propagators, (2) self-energy calculation, (3)
> Dyson's formula, (4) renormalized propagators, (5) LSZ reduction
> formula. You still haven't said whether you are familiar with any of
> these. If you are not, you have to learn about them and how to use
> them before you can do this kind of calculation.
>

I have been hesitating to answer your question about my
familiarity with the QFT method, because no matter how
familiar I would say I am, that does not prove that I am right.
But since you insist, here is some information on my
academic training and research experience.

In my graduate program, I have been through one year (two
semesters) of QFT course with Peskin &Schroeder
covering all the QFT methods you have mentioned. And
a semester of Elementary Particle course and one year of
Nuclear Theory which have dealt with some related
calculations. Also I have years of research experience
working in high energy area.

As I have answered your question, could you let me know
your academic training of QFT and any research experience
in high energy area?

> Just to clarify, again, (massless,SM) will give the same result as
> (massive,SM), while (massless,QED) will give the same result as
> (massive,QED). On the other hand, the results of (massles/massive,SM)
> will be different from (massless/massive,QED), simply because SM and
> QED are different field theories.

Since you have claimed SM calculations are different from
QED ones, could you specify the exact result of SM
calculation corresponding to QED P&S (5.13) up to second
order?

Thanks,
J.C. Yoon
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