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View Full Version : Q: P&S p187 eq(6.35)

MM
May29-04, 11:56 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>In Peskin & Schroeder, p187, near the middle of the page,\nthere\'s an equation (6.35) as follows:\n\niM = +ie[u^bar(p\')(gamma^i F_1 + 1/2m i sigma^i^nu F_2) u(p)] A^i_cl(q)\n(6.35)\nImmediately after this equation, P&S write:\n\n"The expression in brackets vanishes at {bold}q = 0, ...."\n\nP&S seem to think this needs no further elaboration, but I\ndon\'t see why their statement is true. Can anyone help me out?\n\nTIA.\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>In Peskin & Schroeder, p187, near the middle of the page,
there's an equation (6.35) as follows:

iM = +ie[u^{bar}(p')(\gamma^i F_1 + 1/2m i \sigma^i^\nu F_2) u(p)] A^{i_}{cl}(q)(6.35)[/itex]
Immediately after this equation, P&S write:

"The expression in brackets vanishes at {bold}q [itex]= 0, ...."

P&S seem to think this needs no further elaboration, but I
don't see why their statement is true. Can anyone help me out?

TIA.
Rene Meyer
May31-04, 06:26 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>\nOn Sat, 29 May 2004 16:56:32 +0000 (UTC), MM wrote:\n&gt; iM =3D +ie[u^bar(p\')(gamma^i F_1 + 1/2m i sigma^i^nu F_2) u(p)] A^i_c=\nl(q)\n&gt; "The expression in brackets vanishes at {bold}q =3D 0, ...."\n\nI think, what they mean is that their S-Matrix is defined as=20\nS_fi =3D delta_fi + iT_fi, and if there is no momentum transfer (q =3D 0)=\n, then\n\nS_fi =3D delta_fi\n\nthis means that T_fi =3D 0 in first order approximation. That is M =3D 0\ntoo, and this means that your bracket vanishes.\n\nI don\'t have the book here now, so correct me if I\'m wrong.\n\nRen=E9.\n\n--=20\nRen=E9 Meyer\nStudent of Physics & Mathematics\nZhejiang University, Hangzhou, China\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Sat, 29 May 2004 16:56:32 +0000 (UTC), MM wrote:
> iM =3D +ie[u^{bar}(p')(\gamma^i F_1 + 1/2m i \sigma^i^\nu F_2) u(p)] A^{i_c}=l(q)
> "The expression in brackets vanishes at {bold}q =3D 0, ...."

I think, what they mean is that their S-Matrix is defined as=20S_{fi} =3D \delta_fi + iT_fi, and if there is no momentum transfer (q =3D 0)=
, then

S_{fi} =3D \delta_fi

this means that T_{fi} =3D in first order approximation. That is M =3D
too, and this means that your bracket vanishes.

I don't have the book here now, so correct me if I'm wrong.

Ren=E9.

--=20
Ren=E9 Meyer
Student of Physics & Mathematics
Zhejiang University, Hangzhou, China