DW
Sep19-04, 06:55 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>\nThe Cartan Metric is defined as\n\\eta_{i,j}=Tr(G_iG_j)\nwhere G_i,G_j are generators of a Lie group in a certain representation,\nTr is to take trace.\n\nMy question is:\nIf we are dealing with quantum mechanics, then G_i,G_j can be operators\n(is this correct?) for example, the angular momentum operator. What is\nthe physical meaning of Cartan Metric for this case?\n\nThanks!\nDW\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>The Cartan Metric is defined as
\eta_{i,j}=Tr(G_{iG_j})
where G_i,G_j are generators of a Lie group in a certain representation,
Tr is to take trace.
My question is:
If we are dealing with quantum mechanics, then G_i,G_j can be operators
(is this correct?) for example, the angular momentum operator. What is
the physical meaning of Cartan Metric for this case?
Thanks!
DW
\eta_{i,j}=Tr(G_{iG_j})
where G_i,G_j are generators of a Lie group in a certain representation,
Tr is to take trace.
My question is:
If we are dealing with quantum mechanics, then G_i,G_j can be operators
(is this correct?) for example, the angular momentum operator. What is
the physical meaning of Cartan Metric for this case?
Thanks!
DW