Re: Moyal product and differential equations [Archive]

Aaron Bergman

Jun7-04, 12:36 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 <daf5b86f.0406050750.59e9e12f@posting.google.com>, \nsoroastro2001@yahoo.co.uk (David) wrote:\n\n> Hello,\n>\n> I have a (functional) differential equation involving a Moyal product\n> that I would like to solve. Could anyone suggest any literature on\n> analysis with the Moyal product?\n\nFunctions multiplied by the Moyal product can be mapped to products of\noperators (look up Weyl map IIRC). In other words, I\'d say to try to\nturn it into a quantum mechanics problem.\n\nAaron\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 <daf5b86f.0406050750.59e9e12f@posting.google.com>,
soroastro2001@yahoo.co.uk (David) wrote:

> Hello,
>
> I have a (functional) differential equation involving a Moyal product
> that I would like to solve. Could anyone suggest any literature on
> analysis with the Moyal product?

Functions multiplied by the Moyal product can be mapped to products of
operators (look up Weyl map IIRC). In other words, I'd say to try to
turn it into a quantum mechanics problem.

Aaron

David

Jun8-04, 04:03 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>\nAaron Bergman <abergman@physics.utexas.edu> wrote in message news:<abergman-536871.16532506062004@localhost>...\n\n> In article <daf5b86f.0406050750.59e9e12f@posting.google.com>, \n> soroastro2001@yahoo.co.uk (David) wrote:\n\n> > I have a (functional) differential equation involving a Moyal product\n> > that I would like to solve. Could anyone suggest any literature on\n> > analysis with the Moyal product?\n>\n> Functions multiplied by the Moyal product can be mapped to products of\n> operators (look up Weyl map IIRC). In other words, I\'d say to try to\n> turn it into a quantum mechanics problem.\n\nThanks! As it turns out, this is essentially the route I\'d gone\nthrough to get to the Moyal product. Maybe this means I\'ll have\nbetter luck leaving everything in terms of explicit operators.\n\nSomething I had in mind was that star products seem to be appearing\nmore these days because of work on NCFT. This seems to have something\nto do with the low energy dynamics of string theory with background NS\nfields switched on, but I\'m not familiar with the details. I was\nhoping that perhaps calculational techniques had been devised to cope\nwith actions where the elementary fields appear with multiplication\nunder a star product?\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>Aaron Bergman <abergman@physics.utexas.edu> wrote in message news:<abergman-536871.16532506062004@localhost>...

> In article <daf5b86f.0406050750.59e9e12f@posting.google.com>,
> soroastro2001@yahoo.co.uk (David) wrote:

> > I have a (functional) differential equation involving a Moyal product
> > that I would like to solve. Could anyone suggest any literature on
> > analysis with the Moyal product?
>
> Functions multiplied by the Moyal product can be mapped to products of
> operators (look up Weyl map IIRC). In other words, I'd say to try to
> turn it into a quantum mechanics problem.

Thanks! As it turns out, this is essentially the route I'd gone
through to get to the Moyal product. Maybe this means I'll have
better luck leaving everything in terms of explicit operators.

Something I had in mind was that star products seem to be appearing
more these days because of work on NCFT. This seems to have something
to do with the low energy dynamics of string theory with background NS
fields switched on, but I'm not familiar with the details. I was
hoping that perhaps calculational techniques had been devised to cope
with actions where the elementary fields appear with multiplication
under a star product?

arivero

Jun14-04, 02:50 PM

No a calculational technique precisely, but let me to mention a recent paper from Gayral, Gracia-Bondia et al, title "Moyal Planes are Spectral Triples". hep-th/0307241