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Dean
May12-04, 01:49 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>OK, so I\'ve tried to read Thiemann\'s papers on the Hamiltonian\nconstraint, and from what I can gather (thanks to Baez\'s wee article),\nhe showed that it *can* be quantized. But there are certain problems:\nthe quantum constraint algebra is not isomorphic to the classical\nconstraint algebra; its `covariantization\' is dodgy, and so on. This is\nall quite old news now (in physics terms), so I would like to know what\nthe current state of play is. What is the verdict on Thiemann\'s Master\nConstraint programme? What of the spin-foam models: do they resolve the\nissue? (I got the impression from Smolin at a recent conference that he\nthought Yes), do they relate to what Thiemann has been working on\nlately? What of the Chern-Simons, Knot theory connections? (I do wish\nJohn Baez and Javier Munian would write a sequel carrying on from where\nthey left off: that would solve all of my problems!) Are we any further\non from Thiemann\'s original insight?\n\n\nTa,\n\nDean\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>OK, so I've tried to read Thiemann's papers on the Hamiltonian
constraint, and from what I can gather (thanks to Baez's wee article),
he showed that it *can* be quantized. But there are certain problems:
the quantum constraint algebra is not isomorphic to the classical
constraint algebra; its `covariantization' is dodgy, and so on. This is
all quite old news now (in physics terms), so I would like to know what
the current state of play is. What is the verdict on Thiemann's Master
Constraint programme? What of the spin-foam models: do they resolve the
issue? (I got the impression from Smolin at a recent conference that he
thought Yes), do they relate to what Thiemann has been working on
lately? What of the Chern-Simons, Knot theory connections? (I do wish
John Baez and Javier Munian would write a sequel carrying on from where
they left off: that would solve all of my problems!) Are we any further
on from Thiemann's original insight?


Ta,

Dean
John Baez
May17-04, 07:39 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>About the Hamiltonian constraint in quantum gravity:\n\nIn article &lt;2004050701510316807%phldpr@leedsacuk&gt;,\nDean &lt;phldpr@leeds.ac.uk&gt; wrote:\n\n&gt;What is the verdict on Thiemann\'s Master Constraint programme?\n\nThe verdict isn\'t in: Thiemann presented the latest results from\nthis program in Marseille earlier this month, and it looks like\nthere\'s a lot of work left before we know if it\'ll work.\n\n&gt;What of the spin-foam models: do they resolve the issue?\n\nNot yet: if we had a spin foam model we trusted, we could\nin principle use it to construct a projection operator onto\nthe space of solutions of the Hamiltonian constraint...\nbut the key words are "if" and "in principle".\n\n&gt;do they relate to what Thiemann has been working on lately?\n\nNobody knows.\n\n&gt;What of the Chern-Simons, Knot theory connections?\n\nNOBODY UNDERSTANDS THE HAMILTONIAN CONSTRAINT!\n\nThere, I hope that\'s clear enough. :-)\n\n&gt;(I do wish John Baez and Javier Munian would write a sequel carrying\n&gt;on from where they left off: that would solve all of my problems!)\n\nThat\'s flattering, but I\'ve decided I want to wait \'til we get a\nworking theory of quantum gravity before I write another book in\nthat direction. (Where "working" just means that it can be shown\nto reduce to general relativity in a suitable limit, not that it\'s\nknown to be physically correct.)\n\n&gt;Are we any further on from Thiemann\'s original insight?\n\nYes, but not much. Some of the best progress has come from Martin\nBojowald, who has applied Thiemann\'s ideas to highly symmetric solutions\nof Einstein\'s equation, like the kind people study in cosmology, and\ngotten some good results. See for example:\n\nMartin Bojowald\nLoop Quantum Cosmology: Recent Progress\nhttp://www.arxiv.org/abs/gr-qc/0402053\n\nYou should also look at this:\n\nAbhay Ashtekar, Jerzy Lewandowski\nBackground Independent Quantum Gravity: A Status Report\nhttp://www.arxiv.org/abs/gr-qc/0404018\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>About the Hamiltonian constraint in quantum gravity:

In article <2004050701510316807%phldpr@leedsacuk>,
Dean <phldpr@leeds.ac.uk> wrote:

>What is the verdict on Thiemann's Master Constraint programme?

The verdict isn't in: Thiemann presented the latest results from
this program in Marseille earlier this month, and it looks like
there's a lot of work left before we know if it'll work.

>What of the spin-foam models: do they resolve the issue?

Not yet: if we had a spin foam model we trusted, we could
in principle use it to construct a projection operator onto
the space of solutions of the Hamiltonian constraint...
but the key words are "if" and "in principle".

>do they relate to what Thiemann has been working on lately?

Nobody knows.

>What of the Chern-Simons, Knot theory connections?

NOBODY UNDERSTANDS THE HAMILTONIAN CONSTRAINT!

There, I hope that's clear enough. :-)

>(I do wish John Baez and Javier Munian would write a sequel carrying
>on from where they left off: that would solve all of my problems!)

That's flattering, but I've decided I want to wait 'til we get a
working theory of quantum gravity before I write another book in
that direction. (Where "working" just means that it can be shown
to reduce to general relativity in a suitable limit, not that it's
known to be physically correct.)

>Are we any further on from Thiemann's original insight?

Yes, but not much. Some of the best progress has come from Martin
Bojowald, who has applied Thiemann's ideas to highly symmetric solutions
of Einstein's equation, like the kind people study in cosmology, and
gotten some good results. See for example:

Martin Bojowald
Loop Quantum Cosmology: Recent Progress
http://www.arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0402053

You should also look at this:

Abhay Ashtekar, Jerzy Lewandowski
Background Independent Quantum Gravity: A Status Report
http://www.arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0404018