Orbis T.
Apr28-04, 02:26 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>\nHi,\n\nWriting the antisymmetric (f_{jkl}) and symmetric\n(d_{jkl}) structure constants of the Lie algebra of\nSU(N) (determined by the generators F_{m}) as\nfollows:\n\nf_{jkl} = - (i / 4) Tr([F_{j},F_{k}]_{-} F_{l})\n\nand\n\nd_{jkl} = (1 / 4) Tr([F_{j},F_{k}]_{+} F_{l})\n\nrespectively, one can then obtain the following\nidentities:\n\na) f_{jkl} d_{lmn} + f_{nkl} d_{lmj} +\nf_{mkl}d_{jln}\n= 0\n\nb) f_{jkl} f_{lmn} + f_{mkl} f_{lnj} +\nf_{jml}f_{lnk}\n= 0\n\nThe identity a) contains both symmetric and\nantisymmetric structure constants while b) contains\nonly antisymmetric constants.\n\nIs there some identity of the kind of b) (or\nsimilar)\nbut involving only the symmetric structure\nconstants?\nCould you recommend me a good book where I could\nlearn\na bit about general properties of the Lie algebra of\nSU(N) (I have been reading some books of Group\nTheory\nfor physicists but they are usually restricted to\nthe\ncase N \\leq 5).\n\nbest,\n\nOrbis\n\n\n\n\n\n_________________ _________________\nDo you Yahoo!?\nWin a \\$20,000 Career Makeover at Yahoo! HotJobs\nhttp://hotjobs.sweepstakes.yahoo.com/careermakeover\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>Hi,
Writing the antisymmetric (f_{jkl}) and symmetric
(d_{jkl}) structure constants of the Lie algebra of
SU(N) (determined by the generators F_{m}) as
follows:
f_{jkl} = - (i / 4) Tr([F_{j},F_{k}]_{-} F_{l})
and
d_{jkl} = (1 / 4) Tr([F_{j},F_{k}]_{+} F_{l})
respectively, one can then obtain the following
identities:
a) f_{jkl} d_{lmn} + f_{nkl} d_{lmj} +f_{mkl}d_{jln}
=
b) f_{jkl} f_{lmn} + f_{mkl} f_{lnj} +f_{jml}f_{lnk}
=
The identity a) contains both symmetric and
antisymmetric structure constants while b) contains
only antisymmetric constants.
Is there some identity of the kind of b) (or
similar)
but involving only the symmetric structure
constants?
Could you recommend me a good book where I could
learn
a bit about general properties of the Lie algebra of
SU(N) (I have been reading some books of Group
Theory
for physicists but they are usually restricted to
the
case N \leq 5).
best,
Orbis
__{________________________________}
Do you Yahoo!?
Win a $20,000 Career Makeover at Yahoo! HotJobs
http://hotjobs.sweepstakes.yahoo.com/careermakeover
Writing the antisymmetric (f_{jkl}) and symmetric
(d_{jkl}) structure constants of the Lie algebra of
SU(N) (determined by the generators F_{m}) as
follows:
f_{jkl} = - (i / 4) Tr([F_{j},F_{k}]_{-} F_{l})
and
d_{jkl} = (1 / 4) Tr([F_{j},F_{k}]_{+} F_{l})
respectively, one can then obtain the following
identities:
a) f_{jkl} d_{lmn} + f_{nkl} d_{lmj} +f_{mkl}d_{jln}
=
b) f_{jkl} f_{lmn} + f_{mkl} f_{lnj} +f_{jml}f_{lnk}
=
The identity a) contains both symmetric and
antisymmetric structure constants while b) contains
only antisymmetric constants.
Is there some identity of the kind of b) (or
similar)
but involving only the symmetric structure
constants?
Could you recommend me a good book where I could
learn
a bit about general properties of the Lie algebra of
SU(N) (I have been reading some books of Group
Theory
for physicists but they are usually restricted to
the
case N \leq 5).
best,
Orbis
__{________________________________}
Do you Yahoo!?
Win a $20,000 Career Makeover at Yahoo! HotJobs
http://hotjobs.sweepstakes.yahoo.com/careermakeover