Calculational problem in Peskin/Schroeder QFT [Archive]

Rene Meyer

Aug26-04, 04:30 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>Hi,\n\ncan anyone help me with the last step in Eq. 3.49 of P&S QFT? How does\nthe \\sqrt{E \\pm p^3} come in play here?\n\nRene.\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>Hi,

can anyone help me with the last step in Eq. 3.49 of P&S QFT? How does
the \sqrt{E \pm p^3} come in play here?

Rene.

DW

Aug27-04, 02:42 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>p^3 is the third constitute of the momentum.\nIt is sqrt(m)*exp(\\eta/2)=sqrt(m*exp(\\eta))\n=sqrt(m*cosh(\\eta))+m*sinh (\\eta)) and notice\nequation(3.48).\n\nRene Meyer wrote:\n> Hi,\n>\n> can anyone help me with the last step in Eq. 3.49 of P&S QFT? How does\n> the \\sqrt{E \\pm p^3} come in play here?\n>\n> Rene.\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>p^3 is the third constitute of the momentum.
It is \sqrt(m)*\exp(\eta/2)=\sqrt(m*\exp(\eta))=\sqrt(m*cosh(\eta))+m*sinh( \eta)) and notice
equation(3.48).

Rene Meyer wrote:
> Hi,
>
> can anyone help me with the last step in Eq. 3.49 of P&S QFT? How does
> the \sqrt{E \pm p^3} come in play here?
>
> Rene.
>

MM

Aug27-04, 06:10 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>\n\nRene Meyer asked:\n\n> can anyone help me with the last step in Eq. 3.49 of P&S QFT?\n> How does the \\sqrt{E \\pm p^3} come in play here?\n\nDoesn\'t it follow from eq(3.48)? I.e:....\n\nE = m cosh(eta)\np^3 = m sinh(eta)\n\ntherefore:\n\nE + p^3 = m exp(eta)\n\nsqrt(E + p^3) = exp(eta/2) sqrt(m)\n\nand similarly for E - p^3.\n\n\n(BTW, if you have any other issues with P&S chapters 2-6,\nfeel free to email me if you\'d like a faster response.\nI worked through those chapters in excruciating detail\nearlier this year. :-)\n\n\n- MikeM\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>Rene Meyer asked:

> can anyone help me with the last step in Eq. 3.49 of P&S QFT?
> How does the \sqrt{E \pm p^3} come in play here?

Doesn't it follow from eq(3.48)? I.e:....

E = m cosh(\eta)p^3 = m sinh(\eta)

therefore:

E + p^3 = m \exp(\eta)\sqrt(E + p^3) = \exp(\eta/2) \sqrt(m)

and similarly for E - p^3.

(BTW, if you have any other issues with P&S chapters 2-6,
feel free to email me if you'd like a faster response.
I worked through those chapters in excruciating detail
earlier this year. :-)

- MikeM