View Full Version : Automation of QED perturbation expansions
<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>What is a good reference for the state of the art on this?\n\nMore specifically, has someone written a computer program\nthat will show all the distinct Feynman diagrams at\na given order alpha^n for *any* well-measured QED effect?\n\nI know that one has to remove infinities and then actually compute\nwhat remains, but I am curious if this first step is well-automated now.\n\nIf this first step can be done, can program go on to automatically organize\nthe renormalization procedure so that one is left with a bunch of\nintegrals which are guaranteed finite? Let\'s call this the second step.\nOr does this require a human?\n\nIn other words, can you ask the program to generate\nthe coefficient C_n of alpha^n as a sum of\nunevaluated integrals, which I accept may be quite difficult to compute, but\nwhich are\nguaranteed finite? Say for n = 15?\n\nIf the answer is no to the second step, what are the main difficulties?\n\nregards,\nalan\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>What is a good reference for the state of the art on this?
More specifically, has someone written a computer program
that will show all the distinct Feynman diagrams at
a given order \alpha^n for *any* well-measured QED effect?
I know that one has to remove infinities and then actually compute
what remains, but I am curious if this first step is well-automated now.
If this first step can be done, can program go on to automatically organize
the renormalization procedure so that one is left with a bunch of
integrals which are guaranteed finite? Let's call this the second step.
Or does this require a human?
In other words, can you ask the program to generate
the coefficient C_n of \alpha^n as a sum of
unevaluated integrals, which I accept may be quite difficult to compute, but
which are
guaranteed finite? Say for n = 15?
If the answer is no to the second step, what are the main difficulties?
regards,
alan
Danny Ross Lunsford
Apr19-04, 02:18 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>Alan wrote:\n\n> What is a good reference for the state of the art on this?\n>\n> More specifically, has someone written a computer program\n> that will show all the distinct Feynman diagrams at\n> a given order alpha^n for *any* well-measured QED effect?\n>\n> I know that one has to remove infinities and then actually compute\n> what remains, but I am curious if this first step is well-automated now.\n\nGood question, I\'d love to look at that code.\n\nAs I understand it, the number of diagrams to evaluate increases so\nrapidly that even the strongest computers are soon overwhelmed.\n\nI saw an interview with a physicist who was being honest (imagine!).\nWhen the subject of "wave function of the Universe" came up, he pointed\nout that calculating the interaction of 300 objects to some low order\nwould involve more terms than there are particles in the Universe.\n\n-drl\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>Alan wrote:
> What is a good reference for the state of the art on this?
>
> More specifically, has someone written a computer program
> that will show all the distinct Feynman diagrams at
> a given order \alpha^n for *any* well-measured QED effect?
>
> I know that one has to remove infinities and then actually compute
> what remains, but I am curious if this first step is well-automated now.
Good question, I'd love to look at that code.
As I understand it, the number of diagrams to evaluate increases so
rapidly that even the strongest computers are soon overwhelmed.
I saw an interview with a physicist who was being honest (imagine!).
When the subject of "wave function of the Universe" came up, he pointed
out that calculating the interaction of 300 objects to some low order
would involve more terms than there are particles in the Universe.
-drl
Matthew A. Nobes
Apr19-04, 02:18 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 article <Cq2dncgv1_2k5BzdRVn-uQ@adelphia.com>, Alan wrote:\n> What is a good reference for the state of the art on this?\n\nFor QED you probably want to look up some of the papers by\nKinoshita. Start with his book "Quantum Electrodynamics"\nfrom around 1990.\n\n> More specifically, has someone written a computer program\n> that will show all the distinct Feynman diagrams at\n> a given order alpha^n for *any* well-measured QED effect?\n>\n> I know that one has to remove infinities and then actually compute\n> what remains, but I am curious if this first step is well-automated now.\n>\n> If this first step can be done, can program go on to automatically organize\n> the renormalization procedure so that one is left with a bunch of\n> integrals which are guaranteed finite? Let\'s call this the second step.\n> Or does this require a human?\n>\n> In other words, can you ask the program to generate\n> the coefficient C_n of alpha^n as a sum of\n> unevaluated integrals, which I accept may be quite difficult to compute, but\n> which are\n> guaranteed finite? Say for n = 15?\n\nThe answer to this is no.\n\n> If the answer is no to the second step, what are the main difficulties?\n\nThere are a number of difficulties. The first is that you have to extract\nthe dvergences of the integrals and remove them with counterterms.\nOne place you might want to look is in some of the documentation and\npapers about Feynarts/Feyncalc. These are mathmatica packages for\ncomputing standard model processes.\n\nThere are numerical issuse as well. As you get to higher and higher\noders the infrared divergences get stronger. The whole answer is\nIR finite, but you end up looking for tiny differences. In his\nbook Kinoshita describes how to do this. He ended up having to use\nquadruple precision accuracy which slows things down a lot.\n\n--\nmanobes@sdf.lonestar.org\nSDF Public Access UNIX System - http://sdf.lonestar.org\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>In article <Cq2dncgv1_2k5BzdRVn-uQ@adelphia.com>, Alan wrote:
> What is a good reference for the state of the art on this?
For QED you probably want to look up some of the papers by
Kinoshita. Start with his book "Quantum Electrodynamics"
from around 1990.
> More specifically, has someone written a computer program
> that will show all the distinct Feynman diagrams at
> a given order \alpha^n for *any* well-measured QED effect?
>
> I know that one has to remove infinities and then actually compute
> what remains, but I am curious if this first step is well-automated now.
>
> If this first step can be done, can program go on to automatically organize
> the renormalization procedure so that one is left with a bunch of
> integrals which are guaranteed finite? Let's call this the second step.
> Or does this require a human?
>
> In other words, can you ask the program to generate
> the coefficient C_n of \alpha^n as a sum of
> unevaluated integrals, which I accept may be quite difficult to compute, but
> which are
> guaranteed finite? Say for n = 15?
The answer to this is no.
> If the answer is no to the second step, what are the main difficulties?
There are a number of difficulties. The first is that you have to extract
the dvergences of the integrals and remove them with counterterms.
One place you might want to look is in some of the documentation and
papers about Feynarts/Feyncalc. These are mathmatica packages for
computing standard model processes.
There are numerical issuse as well. As you get to higher and higher
oders the infrared divergences get stronger. The whole answer is
IR finite, but you end up looking for tiny differences. In his
book Kinoshita describes how to do this. He ended up having to use
quadruple precision accuracy which slows things down a lot.
--
manobes@sdf.lonestar.org
SDF Public Access UNIX System - http://sdf.lonestar.org
Arnold Neumaier
Apr19-04, 01:28 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>Danny Ross Lunsford wrote:\n\n> As I understand it, the number of diagrams to evaluate increases so\n> rapidly that even the strongest computers are soon overwhelmed.\n>\n> I saw an interview with a physicist who was being honest (imagine!).\n> When the subject of "wave function of the Universe" came up, he pointed\n> out that calculating the interaction of 300 objects to some low order\n> would involve more terms than there are particles in the Universe.\n\nBut we routinely calculate the interaction of 10^23 objects to some\nlow order, using statistical mechanics.\n\nOnly detailed scattering of many objects is exceedingly hard.\nBut who cares about predicting the details of an explosion?\nOne is usually interested in a small amount of gross information,\nand this is available much easier.\n\n\nArnold Neumaier\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>Danny Ross Lunsford wrote:
> As I understand it, the number of diagrams to evaluate increases so
> rapidly that even the strongest computers are soon overwhelmed.
>
> I saw an interview with a physicist who was being honest (imagine!).
> When the subject of "wave function of the Universe" came up, he pointed
> out that calculating the interaction of 300 objects to some low order
> would involve more terms than there are particles in the Universe.
But we routinely calculate the interaction of 10^23 objects to some
low order, using statistical mechanics.
Only detailed scattering of many objects is exceedingly hard.
But who cares about predicting the details of an explosion?
One is usually interested in a small amount of gross information,
and this is available much easier.
Arnold Neumaier
<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>"Matthew A. Nobes" <manobes@vinland.freeshell.org> wrote in message\nnews:slrnc857ph.mtr.manobes@vinland.frees hell.org...\n> In article <Cq2dncgv1_2k5BzdRVn-uQ@adelphia.com>, Alan wrote:\n> > What is a good reference for the state of the art on this?\n>\n> For QED you probably want to look up some of the papers by\n> Kinoshita. Start with his book "Quantum Electrodynamics"\n> from around 1990.\n\nThank you for the reference.\nI\'m getting his book and I got a sense of what can\nbe done now with his hep-ph/0402206.\n\nI see that the final (high order) integrations can only be done with a Monte\nCarlo method.\nThat suggests each additional digit of accuracy now requires a 10 to 100\nfold increase\nin computer power. If that takes 5-10 years, then each new generation of\nphysicists can\nadd at best a couple of digits.\n\nPlus, I got a crude sense from the reference that current\ncomputations are entering a regime where good strong/weak corrections are\nimportant.\nWill that kill the whole program or can people do decent QCD (lattice?)\ncomputations\nnow?\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>"Matthew A. Nobes" <manobes@vinland.freeshell.org> wrote in message
news:slrnc857ph.mtr.manobes@vinland.freeshell.org. ..
> In article <Cq2dncgv1_2k5BzdRVn-uQ@adelphia.com>, Alan wrote:
> > What is a good reference for the state of the art on this?
>
> For QED you probably want to look up some of the papers by
> Kinoshita. Start with his book "Quantum Electrodynamics"
> from around 1990.
Thank you for the reference.
I'm getting his book and I got a sense of what can
be done now with his http://www.arxiv.org/abs/hep-ph/0402206.
I see that the final (high order) integrations can only be done with a Monte
Carlo method.
That suggests each additional digit of accuracy now requires a 10 to 100
fold increase
in computer power. If that takes 5-10 years, then each new generation of
physicists can
add at best a couple of digits.
Plus, I got a crude sense from the reference that current
computations are entering a regime where good strong/weak corrections are
important.
Will that kill the whole program or can people do decent QCD (lattice?)
computations
now?
Arnold Neumaier
Apr22-04, 02:50 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>Alan wrote:\n> "Matthew A. Nobes" <manobes@vinland.freeshell.org> wrote in message\n> news:slrnc857ph.mtr.manobes@vinland.freeshell.org. ..\n>\n>>In article <Cq2dncgv1_2k5BzdRVn-uQ@adelphia.com>, Alan wrote:\n>>\n>>>What is a good reference for the state of the art on this?\n>>\n>>For QED you probably want to look up some of the papers by\n>>Kinoshita. Start with his book "Quantum Electrodynamics"\n>>from around 1990.\n>\n>\n> Thank you for the reference.\n> I\'m getting his book and I got a sense of what can\n> be done now with his hep-ph/0402206.\n>\n> Plus, I got a crude sense from the reference that current\n> computations are entering a regime where good strong/weak corrections are\n> important.\n> Will that kill the whole program or can people do decent QCD (lattice?)\n> computations\n> now?\n\nProbably (but this is just a guess) it is enough to use experimentally\navailable form factors instead of real QCD calculations.\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>Alan wrote:
> "Matthew A. Nobes" <manobes@vinland.freeshell.org> wrote in message
> news:slrnc857ph.mtr.manobes@vinland.freeshell.org. ..
>
>>In article <Cq2dncgv1_2k5BzdRVn-uQ@adelphia.com>, Alan wrote:
>>
>>>What is a good reference for the state of the art on this?
>>
>>For QED you probably want to look up some of the papers by
>>Kinoshita. Start with his book "Quantum Electrodynamics"
>>from around 1990.
>
>
> Thank you for the reference.
> I'm getting his book and I got a sense of what can
> be done now with his http://www.arxiv.org/abs/hep-ph/0402206.
>
> Plus, I got a crude sense from the reference that current
> computations are entering a regime where good strong/weak corrections are
> important.
> Will that kill the whole program or can people do decent QCD (lattice?)
> computations
> now?
Probably (but this is just a guess) it is enough to use experimentally
available form factors instead of real QCD calculations.
Arnold Neumaier
Matthew A. Nobes
Apr22-04, 03:03 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>In article <Y5adnXX9xoYVlBndRVn-tA@adelphia.com>, Alan wrote:\n\n> I see that the final (high order) integrations can only be done with a Monte\n> Carlo method.\n\nYes, you have to use Monte Carlo integration (VEGAS) to do the multidimensional\nintegrals. Plus, as I said, the accuracy has to be quadpruple (or better)\nprecision in order to treat the IR divergences correctly.\n\n> That suggests each additional digit of accuracy now requires a 10 to 100\n> fold increase\n> in computer power. If that takes 5-10 years, then each new generation of\n> physicists can\n> add at best a couple of digits.\n\nTo put a positive spin on that it should be noted that this roughly\npaces the experiments.\n\n> Plus, I got a crude sense from the reference that current\n> computations are entering a regime where good strong/weak corrections are\n> important.\n\nYes. The weak contributions are not a fundemental problem though, since\nthey can be done perturbativly.\n\n> Will that kill the whole program or can people do decent QCD (lattice?)\n> computations now?\n\nThe lattice calculations are hard, but as far as I know, not impossible.\nThere are lattice people thinking about this, but I\'m not one of them.\n\n--\nmanobes@sdf.lonestar.org\nSDF Public Access UNIX System - http://sdf.lonestar.org\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>In article <Y5adnXX9xoYVlBndRVn-tA@adelphia.com>, Alan wrote:
> I see that the final (high order) integrations can only be done with a Monte
> Carlo method.
Yes, you have to use Monte Carlo integration (VEGAS) to do the multidimensional
integrals. Plus, as I said, the accuracy has to be quadpruple (or better)
precision in order to treat the IR divergences correctly.
> That suggests each additional digit of accuracy now requires a 10 to 100
> fold increase
> in computer power. If that takes 5-10 years, then each new generation of
> physicists can
> add at best a couple of digits.
To put a positive spin on that it should be noted that this roughly
paces the experiments.
> Plus, I got a crude sense from the reference that current
> computations are entering a regime where good strong/weak corrections are
> important.
Yes. The weak contributions are not a fundemental problem though, since
they can be done perturbativly.
> Will that kill the whole program or can people do decent QCD (lattice?)
> computations now?
The lattice calculations are hard, but as far as I know, not impossible.
There are lattice people thinking about this, but I'm not one of them.
--
manobes@sdf.lonestar.org
SDF Public Access UNIX System - http://sdf.lonestar.org
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