## evaluating QED thru montecarlo

<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>\nHi,\n\nIn Quantum Monte Carlo (QMC) people usually use random walkers in\nR^3n space, where n is the number of particles, which is equivalent to\ncompute observables based on a sampled distribution of spacial\n(position-defined) basis kets\n\nIf one wants to add first QED corrections to such calculations it\nseems one must evaluate quantities like\n\nA_{nu} J^{nu} =\n\n\\PSI* \\gamma^nu \\PSI A_{nu} e^(ikx) alfa*(k)\n\nwhere alfa*(k) is the electromagnetic creation operator on the k mode,\nand the rest is the current of a Dirac spinor\n\nThe technical problem i see to evaluate this quantity is that you need\nto know \\PSI wavefunction to actually perform the computation, which\nis untypical to what one do in Quantum Mechanics in the sense that,\nfor example e^(dt*P^2/2*m) is an operator that does Not rely on the\nphysical wavefunction values to be able to compute transition\nprobabilities/amplitudes\n\nany comments about this feature?\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>Hi,

In Quantum Monte Carlo (QMC) people usually use random walkers in
$R^{3n}$ space, where n is the number of particles, which is equivalent to
compute observables based on a sampled distribution of spacial
(position-defined) basis kets

If one wants to add first QED corrections to such calculations it
seems one must evaluate quantities like

$$A_{\nu} J^{\nu} =\PSI* \gamma^\nu \PSI A_{\nu} e^(ikx) alfa*(k)$$

where $alfa*(k)$ is the electromagnetic creation operator on the k mode,
and the rest is the current of a Dirac spinor

The technical problem i see to evaluate this quantity is that you need
to know $\PSI$ wavefunction to actually perform the computation, which
is untypical to what one do in Quantum Mechanics in the sense that,
for example $e^(dt*P^2/2*m)$ is an operator that does Not rely on the
physical wavefunction values to be able to compute transition
probabilities/amplitudes