Arnold Neumaier
Apr19-04, 01:15 PM
<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>FrediFizzx wrote:\n\n> | Neither. A bare electron is the formal entity discussed in textbooks\n> | when they do perturbative quantum electrodynamics. The intuitive\n> | picture generally given is that a bare electron is surrounded\n> | by a clud of virtual photons and virtual electron-positron pairs\n> | to make up a physical, \'dressed\' electron. Only the latter is real\n> | and observable. The former is a formal caricature of the latter,\n> | with paradoxical properties (infinite mass, etc.).\n> |\n> | On a more substantial level, the observable electrons are produced\n> | from the bare electrons by a process called renormalization,\n> | which modifies the propagators by self-energy terms\n> | and the currents by form factors. As the name says, the latter define\n> | the \'form\' of a particle. (In the above picture, it would correspond\n> | to the shape of the virtual cloud, though it is better to avoid\n> | giving the virtual particles too much of meaning.)\n>\n> Why is it better to "avoid giving the virtual particles too much of meaning"\n> if in fact they are part of the "form" of an observable electron?\n\nThe "form" is the form factor, which is a well-defined physical function\n(though at present computable only in perturbation theory).\nBut the virtual objects are artifacts of the perturbation theory.\nThe figurative virtual objects in QFT are there only because of the\nwell-known limitations of the foundations of QFT. In a nonperturbative\nsetting they wouldn\'t occur at all. This can be sen by comparing with\nQM. One could also do nonrelativistic QM with virtual objects but\nno one does so (except sometimes in motivations for QFT),\nbecause it does not add value to a well-understood theory.\n\nMoreover, virtual objects have strange properires. For example,\nthe coulomb interaction between two electrons is mediated by\nvirtual photons faster than the speed of light, with imaginary masses.\n\n\n> | The observable electrons indeed have structure, since their form\n> | factors are nontrivial. For example, in his book\n> | S. Weinberg,\n> | The quantum theory of fields, Vol. I,\n> | Cambridge University Press, 1995,\n> | Weinberg defines and explicitly computes in (11.3.33) the\n> | \'charge radius\' of a physical electron.\n>\n> And the value of this \'charge radius\' that Weinberg computes is? I don\'t\n> have this book.\n\nWell, he doesn\'t complete the calculation, since he only gives the\nintegral expression without going through the necessary renormalization\ncalculations. I don\'t know of any place where one finds a more\ncomplete calculation. Physicists are usually interesting in other\naspects of the form factors.\n\n\nArnold Neumaier\n\n\n\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>FrediFizzx wrote:
> | Neither. A bare electron is the formal entity discussed in textbooks
> | when they do perturbative quantum electrodynamics. The intuitive
> | picture generally given is that a bare electron is surrounded
> | by a clud of virtual photons and virtual electron-positron pairs
> | to make up a physical, 'dressed' electron. Only the latter is real
> | and observable. The former is a formal caricature of the latter,
> | with paradoxical properties (infinite mass, etc.).
> |
> | On a more substantial level, the observable electrons are produced
> | from the bare electrons by a process called renormalization,
> | which modifies the propagators by self-energy terms
> | and the currents by form factors. As the name says, the latter define
> | the 'form' of a particle. (In the above picture, it would correspond
> | to the shape of the virtual cloud, though it is better to avoid
> | giving the virtual particles too much of meaning.)
>
> Why is it better to "avoid giving the virtual particles too much of meaning"
> if in fact they are part of the "form" of an observable electron?
The "form" is the form factor, which is a well-defined physical function
(though at present computable only in perturbation theory).
But the virtual objects are artifacts of the perturbation theory.
The figurative virtual objects in QFT are there only because of the
well-known limitations of the foundations of QFT. In a nonperturbative
setting they wouldn't occur at all. This can be sen by comparing with
QM. One could also do nonrelativistic QM with virtual objects but
no one does so (except sometimes in motivations for QFT),
because it does not add value to a well-understood theory.
Moreover, virtual objects have strange properires. For example,
the coulomb interaction between two electrons is mediated by
virtual photons faster than the speed of light, with imaginary masses.
> | The observable electrons indeed have structure, since their form
> | factors are nontrivial. For example, in his book
> | S. Weinberg,
> | The quantum theory of fields, Vol. I,
> | Cambridge University Press, 1995,
> | Weinberg defines and explicitly computes in (11.3.33) the
> | 'charge radius' of a physical electron.
>
> And the value of this 'charge radius' that Weinberg computes is? I don't
> have this book.
Well, he doesn't complete the calculation, since he only gives the
integral expression without going through the necessary renormalization
calculations. I don't know of any place where one finds a more
complete calculation. Physicists are usually interesting in other
aspects of the form factors.
Arnold Neumaier
> | Neither. A bare electron is the formal entity discussed in textbooks
> | when they do perturbative quantum electrodynamics. The intuitive
> | picture generally given is that a bare electron is surrounded
> | by a clud of virtual photons and virtual electron-positron pairs
> | to make up a physical, 'dressed' electron. Only the latter is real
> | and observable. The former is a formal caricature of the latter,
> | with paradoxical properties (infinite mass, etc.).
> |
> | On a more substantial level, the observable electrons are produced
> | from the bare electrons by a process called renormalization,
> | which modifies the propagators by self-energy terms
> | and the currents by form factors. As the name says, the latter define
> | the 'form' of a particle. (In the above picture, it would correspond
> | to the shape of the virtual cloud, though it is better to avoid
> | giving the virtual particles too much of meaning.)
>
> Why is it better to "avoid giving the virtual particles too much of meaning"
> if in fact they are part of the "form" of an observable electron?
The "form" is the form factor, which is a well-defined physical function
(though at present computable only in perturbation theory).
But the virtual objects are artifacts of the perturbation theory.
The figurative virtual objects in QFT are there only because of the
well-known limitations of the foundations of QFT. In a nonperturbative
setting they wouldn't occur at all. This can be sen by comparing with
QM. One could also do nonrelativistic QM with virtual objects but
no one does so (except sometimes in motivations for QFT),
because it does not add value to a well-understood theory.
Moreover, virtual objects have strange properires. For example,
the coulomb interaction between two electrons is mediated by
virtual photons faster than the speed of light, with imaginary masses.
> | The observable electrons indeed have structure, since their form
> | factors are nontrivial. For example, in his book
> | S. Weinberg,
> | The quantum theory of fields, Vol. I,
> | Cambridge University Press, 1995,
> | Weinberg defines and explicitly computes in (11.3.33) the
> | 'charge radius' of a physical electron.
>
> And the value of this 'charge radius' that Weinberg computes is? I don't
> have this book.
Well, he doesn't complete the calculation, since he only gives the
integral expression without going through the necessary renormalization
calculations. I don't know of any place where one finds a more
complete calculation. Physicists are usually interesting in other
aspects of the form factors.
Arnold Neumaier