<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>alejandro.rivero wrote:\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<408D7C52.1030903@univie.ac.at>...\n>\n>>http ://www.mat.univie.ac.at/~neum/physics-faq.txt\n>\n>>contains answers to some frequently asked questions from\n>>theoretical physics. They were collected from my answers to\n>>postings to the newsgroup sci.physics.research.\n\nThanks for your comments!\n\n\n> Arnold, I believe that your questions are biased towards HEP:\n\nYou probably mean the answers. My questions are biased towards\nmy interests and what happened to come up in s.p.r. that I felt\ncompetent to answer.\n\n\n> "Current QED and other field theories only claim to model\n> scattering events"\n>\n> Here it is not clear if \'current QED\' is \'the QED of currents\' or\n> \'modern QED\'. If the latter,\n\nYes, I meant \'modern\'. But what you write below shows that my\nstatement was not correct, and I need to phrase more careful.\nThe above was in a context where I thought I didn\'t need to\nbe precise about this. What about saying:\n\n\'\' Modern QED and other field theories are based on modeling\nscattering events.\'\'\n\n\n> you should consider your other statements\n>\n> "The Lamb shift is a non perturbative effect of QED"\n>\n> "[QED] is the theory that was able to reproduce experiments\n> (Lamb shift) with an accuracy of 1 in 10^12"\n>\n> Besides, I am not sure if your view of non-perturbative is the common\n> one. Sometimes it sounds paradoxical:\n>\n> "... is a non perturbative effect of QED. One uses an expansion..."\n>\n\nWhat about the following:\n\nThere is well-defined theory for computing contributions to the\nS-matrix by perturbation theory. There is also much more which uses\nhandwaving arguments and appeals to analogy to compute approximations\nto nonperturbative effects. Examples are:\n- relating the Coulomb interaction and corrections to scattering\namplitudes and then using the nonrelativistic Schroedinger\nequation,\n- computing Lamb shift contributions (now usually done in what is\ncalled the NRQED expansion),\n- Bethe-Salpeter and Schwinger-Dyson equations obtained by resumming\ninfinitely many diagrams.\n\nThe use of \'nonperturbative\' and \'expansion\' together sounds\nparadoxical, but is common terminology in QFT. The term \'perturbative\'\nrefers to results obtained directly from renormalized Feynman graph\nevaluations. From such calculations, one can obtain certain information\n(tree level interactions, form factors, self energies) that can be\nused together with standard QM techniques to study nonperturbative\neffects - generally assuming without clear demonstrations that this\ntransition to QM is allowed.\n\nOf course, although usually called \'nonperturbative\', these techniques\nalso use approximations and expansions. The most conspicous\nhigh accuracy applications (e.g. the Lamb shift) are highly\nnonperturbative. But on a rigorous level, so far only the perturbative\nresults (coefficients of the expansion in coupling constants) have any\nvalidity.\n\n\n>> 1a. Are electrons pointlike/structureless?\n>\n> You extend a lot about charge radius. Perhaps, taking account\n> of Relativistic Quantum theory, a mention of Compton radius\n> should be done, too: pair creation delocalizes a particle by\n> about one half of its compton radius or so. This discussion is\n> typical in modern advanced Quantum Mechanics books.\n\nCan you give a specific reference?\n\n\n>> 1d. How real are \'virtual particles\'?\n>\n> The link to Feynman diagrams seems to me extreme. Surely\n> off-shell particle arguments are previous to Feynman formalism.\n\nYes. I removed the statenment \'were invented\' in this context.\n\n\n> For instance the argument for the short range of Yukawa force\n> is based in virtuality: the quantum of force, say the pion, have\n> a finite mass M and then it is off shell by an energy E = Mc^2.\n> Thus it can exist virtually only for a time less than h/E and in this time\n\nThe time-energy uncertainty relation invoked here has a\ndubious character similar to that of virtual particles.\nIn QFT there is no time operator, hence no formal opportunity\nto introduce an uncertainty relation similar to Heisenberg\'s.\n\n\n> it can travel at most h/E c = h/Mc, again Compton (note here it\n> is not seen as a space-like particle, but as a standard particle\n> that violates energy conservation during a very small time).\n\nNo. If it is taken as off-shell, energy is assumed to be conserved.\nEnergy conservation is the only reason to have it off-shell.\n\n\n> This argument has been always popular.\n\nUnfortunately, \'popular\' cannot be equated with \'sound\'\n\n\n\n>> 1f. ...and decaying particles (resonances)...?\n>\n> Here perhaps Arno Bohm\' view of rigged hilbert\n> spaces as framework for decaying particles could be mentioned.\n\nI added:\nNote that states with complex masses can be handled well in a rigged\nHilbert space (= Gelfand triple) formulation of quantum mechanics.\nResonances appear as so-called Siegert (or Gamov) states.\nA good reference on resonances (not well covered in textbooks) is\nV.I. Kukulin et al.,\nTheory of Resonances,\nKluwer, Dordrecht 1989.\nFor rigged Hilbert spaces (treated in Appendix A of Kukulin), see also\nquant-ph/9805063 and for its functional analysis ramifications,\nK. Maurin,\nGeneral Eigenfunction Expansions and Unitary Representations of\nTopological Groups,\nPWN Polish Sci. Publ., Warsaw 1968.\n\n\n\n>> 3a. Is there a multiparticle relativistic quantum mechanics?\n>\n> Dirac\' many body theory could merit a separate mention. We could\n> discuss if string theory is a MPRQM, but it is not for a FAQ anyway.\n\nWhat is Dirac\'s many body theory? Please give some entry points,\nso that I can check it out.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>alejandro.rivero wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<408D7C52.1030903@univie.ac.at>...
>
>>http://www.mat.univie.ac.at/~neum/physics-faq.txt
>
>>contains answers to some frequently asked questions from
>>theoretical physics. They were collected from my answers to
>>postings to the newsgroup sci.physics.research.
Thanks for your comments!
> Arnold, I believe that your questions are biased towards HEP:
You probably mean the answers. My questions are biased towards
my interests and what happened to come up in s.p.r. that I felt
competent to answer.
> "Current QED and other field theories only claim to model
> scattering events"
>
> Here it is not clear if 'current QED' is 'the QED of currents' or
> 'modern QED'. If the latter,
Yes, I meant 'modern'. But what you write below shows that my
statement was not correct, and I need to phrase more careful.
The above was in a context where I thought I didn't need to
be precise about this. What about saying:
'' Modern QED and other field theories are based on modeling
scattering events.''
> you should consider your other statements
>
> "The Lamb shift is a non perturbative effect of QED"
>
> "[QED] is the theory that was able to reproduce experiments
> (Lamb shift) with an accuracy of 1 in 10^12"
>
> Besides, I am not sure if your view of non-perturbative is the common
> one. Sometimes it sounds paradoxical:
>
> "... is a non perturbative effect of QED. One uses an expansion..."
>
What about the following:
There is well-defined theory for computing contributions to the
S-matrix by perturbation theory. There is also much more which uses
handwaving arguments and appeals to analogy to compute approximations
to nonperturbative effects. Examples are:
- relating the Coulomb interaction and corrections to scattering
amplitudes and then using the nonrelativistic Schroedinger
equation,
- computing Lamb shift contributions (now usually done in what is
called the NRQED expansion),
- Bethe-Salpeter and Schwinger-Dyson equations obtained by resumming
infinitely many diagrams.
The use of 'nonperturbative' and 'expansion' together sounds
paradoxical, but is common terminology in QFT. The term 'perturbative'
refers to results obtained directly from renormalized Feynman graph
evaluations. From such calculations, one can obtain certain information
(tree level interactions, form factors, self energies) that can be
used together with standard QM techniques to study nonperturbative
effects - generally assuming without clear demonstrations that this
transition to QM is allowed.
Of course, although usually called 'nonperturbative', these techniques
also use approximations and expansions. The most conspicous
high accuracy applications (e.g. the Lamb shift) are highly
nonperturbative. But on a rigorous level, so far only the perturbative
results (coefficients of the expansion in coupling constants) have any
validity.
>> 1a. Are electrons pointlike/structureless?
>
> You extend a lot about charge radius. Perhaps, taking account
> of Relativistic Quantum theory, a mention of Compton radius
> should be done, too: pair creation delocalizes a particle by
> about one half of its compton radius or so. This discussion is
> typical in modern advanced Quantum Mechanics books.
Can you give a specific reference?
>> 1d. How real are 'virtual particles'?
>
> The link to Feynman diagrams seems to me extreme. Surely
> off-shell particle arguments are previous to Feynman formalism.
Yes. I removed the statenment 'were invented' in this context.
> For instance the argument for the short range of Yukawa force
> is based in virtuality: the quantum of force, say the pion, have
> a finite mass M and then it is off shell by an energy E = Mc^2.
> Thus it can exist virtually only for a time less than h/E and in this time
The time-energy uncertainty relation invoked here has a
dubious character similar to that of virtual particles.
In QFT there is no time operator, hence no formal opportunity
to introduce an uncertainty relation similar to Heisenberg's.
> it can travel at most h/E c = h/Mc, again Compton (note here it
> is not seen as a space-like particle, but as a standard particle
> that violates energy conservation during a very small time).
No. If it is taken as off-shell, energy is assumed to be conserved.
Energy conservation is the only reason to have it off-shell.
> This argument has been always popular.
Unfortunately, 'popular' cannot be equated with 'sound'
>> 1f. ...and decaying particles (resonances)...?
>
> Here perhaps Arno Bohm' view of rigged hilbert
> spaces as framework for decaying particles could be mentioned.
I added:
Note that states with complex masses can be handled well in a rigged
Hilbert space (= Gelfand triple) formulation of quantum mechanics.
Resonances appear as so-called Siegert (or Gamov) states.
A good reference on resonances (not well covered in textbooks) is
V.I. Kukulin et al.,
Theory of Resonances,
Kluwer, Dordrecht 1989.
For rigged Hilbert spaces (treated in Appendix A of Kukulin), see also
http://www.arxiv.org/abs/quant-ph/9805063 and for its functional analysis ramifications,
K. Maurin,
General Eigenfunction Expansions and Unitary Representations of
Topological Groups,
PWN Polish Sci. Publ., Warsaw 1968.
>> 3a. Is there a multiparticle relativistic quantum mechanics?
>
> Dirac' many body theory could merit a separate mention. We could
> discuss if string theory is a MPRQM, but it is not for a FAQ anyway.
What is Dirac's many body theory? Please give some entry points,
so that I can check it out.
Arnold Neumaier