magnetic field splitting gamma photons in two [Archive]

jdff

Dec9-04, 02:02 AM

Igor Khavkine

Dec10-04, 05:00 AM

<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>On Thu, 09 Dec 2004 08:02:13 +0000, jdff wrote:\n\n> I guess one way of seeing this is as Aharonov-Bohm effect on the electron\n> loop, causing a phase-difference between the two cancelling diagrams. 10^9\n> T is about right for this, because the area it corresponds to equals the\n> length-scale equivalent to the mass-energy of the virtual electron.\n\nThat\'s a good way to put it. This is how this idea would be incorporated\ninto a QED calculation. Usually, the electron propagator is calculated\nstarting from vacuum free solutions of the Dirac equation. However, if we\nhave a strong background field, and the stronger it is the more classical\nit is, what we can do instead is separate the electromagnetic field into a\nbackground and a perturbation. Since the E&M equations are linear, the\nperturbation will have exactly the same quantization as the full field.\nHowever, to get the electron propagator we must now solve the Dirac\nequation *with* a background field. And it is clear that electron and\npositron states can be distinguished when a background field is present.\nThink about an electron and a positron moving in a magnetic field, both\nmove in spirals, but with opposite helicities. Or think of the\nAharonov-Bohm effect.\n\nNow my argument about the cancellation between the triangle graphs with\nopposite internal electron line orientations no longer works. To be\nhonest, I\'ve never done such a calculation explicitly so I\'m not sure the\namount of cancellation between these diagrams is related to the\nAharonov-Bohm effect, but it sounds reasonable for them to be related.\n\nThere is another way to think of this process using virtual photons coming\nfrom the background field. If there aren\'t any takers, I\'ll post my view\nof it later and show that they are essentially the same.\n\nIgor\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>On Thu, 09 Dec 2004 08:02:13 +0000, jdff wrote:

> I guess one way of seeing this is as Aharonov-Bohm effect on the electron
> loop, causing a phase-difference between the two cancelling diagrams. 10^9
> T is about right for this, because the area it corresponds to equals the
> length-scale equivalent to the mass-energy of the virtual electron.

That's a good way to put it. This is how this idea would be incorporated
into a QED calculation. Usually, the electron propagator is calculated
starting from vacuum free solutions of the Dirac equation. However, if we
have a strong background field, and the stronger it is the more classical
it is, what we can do instead is separate the electromagnetic field into a
background and a perturbation. Since the E&M equations are linear, the
perturbation will have exactly the same quantization as the full field.
However, to get the electron propagator we must now solve the Dirac
equation *with* a background field. And it is clear that electron and
positron states can be distinguished when a background field is present.
Think about an electron and a positron moving in a magnetic field, both
move in spirals, but with opposite helicities. Or think of the
Aharonov-Bohm effect.

Now my argument about the cancellation between the triangle graphs with
opposite internal electron line orientations no longer works. To be
honest, I've never done such a calculation explicitly so I'm not sure the
amount of cancellation between these diagrams is related to the
Aharonov-Bohm effect, but it sounds reasonable for them to be related.

There is another way to think of this process using virtual photons coming
from the background field. If there aren't any takers, I'll post my view
of it later and show that they are essentially the same.

Igor