quantum field theory [Archive]

alistair

Aug30-04, 03:25 PM

Arnold Neumaier

Aug31-04, 03:41 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>alistair wrote:\n> In QCD theory, an instanton is a soliton at a particular instant of\n> time.\n> But what is the soliton here - is it a wavefunction? What does the\n> instanton represent physically - a gluon or quark? When theorists\n> say: "switching between vacua" are they talking about changing the\n> number of gluons\n> and their spatial positions?\n\nSolitons are _classical_ solutions of certain hyperbolic equations\n(e.g., the classical Yang-Mills equations in space-time)\nwhile instantons are their Euclidean (imaginary-time) counterparts.\n\nhttp://mathworld.wolfram.com/Soliton.html\nhttp://scienceworld.wolfram.com/physics/Instaton.html\n\nEach classical solution of the field equation represents a possible\nvacuum for a quantum field theory.\n\nI don\'t understand enough about your other questions, but it looks like\nthe answer is always \'No\'.\n\n\nArnold Neumaier\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>alistair wrote:
> In QCD theory, an instanton is a soliton at a particular instant of
> time.
> But what is the soliton here - is it a wavefunction? What does the
> instanton represent physically - a gluon or quark? When theorists
> say: "switching between vacua" are they talking about changing the
> number of gluons
> and their spatial positions?

Solitons are _classical_ solutions of certain hyperbolic equations
(e.g., the classical Yang-Mills equations in space-time)
while instantons are their Euclidean (imaginary-time) counterparts.

http://mathworld.wolfram.com/Soliton.html
http://scienceworld.wolfram.com/physics/Instaton.html

Each classical solution of the field equation represents a possible
vacuum for a quantum field theory.

I don't understand enough about your other questions, but it looks like
the answer is always 'No'.

Arnold Neumaier