PDA

View Full Version : So it is a ordering ambiguity after all.


Alejandro
Aug17-04, 02:00 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>Back from the mountain.\n\nThe GSW is a good book for road reading. I mean, I read the book while\nI walk on the left side in the strip of the road. Then cars coming\nupon me are able to see I am deeply abstracted and they prever to move\nthemselves left instead of trying to get me out of the road. I did\nabout five chapters, sorry I can not give a translation to kilometers\n:-)\n\nNow, from the revelations in the book, the most fascinating thing, to\nme, is that the D=26 condition can be seen to come from an operator\nordering ambiguity.\n\nOrdering ambiguities are deeply geometrical. In the seventees, it was\nshown that the diferent prescriptions for ordering in quantum\nmechanics were equivalent to diferent prescriptions for discretization\nof the derivative in the path integral. Time ago, I conjectured that\nthe generation mechanism (CKM matrix and three generations) was dued\nto some hidden consistency requisite of Nature\' 3+1 field theory,\nasking for 12 fermionic fields to cancel some ambiguity of this kind\n-I speculated far, that the cancelation should involve an action\nprinciple having crossed second derivatives-. It seems that string\ntheoretists got to proof that a kind of 1+1 field theory asks for 26\nbosonic fields.\n\nI wonder how much of the geometric meaning of this aspect of bosonic\nstrings has been worked out. Most works prefer to get out D=26 from\ncancelation of the anomaly, but this other way is most interesting.\n\nAlejandro Rivero\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>Back from the mountain.

The GSW is a good book for road reading. I mean, I read the book while
I walk on the left side in the strip of the road. Then cars coming
upon me are able to see I am deeply abstracted and they prever to move
themselves left instead of trying to get me out of the road. I did
about five chapters, sorry I can not give a translation to kilometers
:-)

Now, from the revelations in the book, the most fascinating thing, to
me, is that the D=26 condition can be seen to come from an operator
ordering ambiguity.

Ordering ambiguities are deeply geometrical. In the seventees, it was
shown that the diferent prescriptions for ordering in quantum
mechanics were equivalent to diferent prescriptions for discretization
of the derivative in the path integral. Time ago, I conjectured that
the generation mechanism (CKM matrix and three generations) was dued
to some hidden consistency requisite of Nature' 3+1 field theory,
asking for 12 fermionic fields to cancel some ambiguity of this kind
-I speculated far, that the cancelation should involve an action
principle having crossed second derivatives-. It seems that string
theoretists got to proof that a kind of 1+1 field theory asks for 26
bosonic fields.

I wonder how much of the geometric meaning of this aspect of bosonic
strings has been worked out. Most works prefer to get out D=26 from
cancelation of the anomaly, but this other way is most interesting.

Alejandro Rivero

arivero
Sep3-04, 04:33 AM
self-quote:
> Now, from the revelations in the book, the most fascinating thing, to
> me, is that the condition can be seen to come from an operator
> ordering ambiguity.

Perhaps I should make clear I was referring to equations 2.3.15 to 2.3.17, where D is derived from a regularised calculation of the normal-ordering constant.

By the way, another atracting thing of the bosonic thery is the tachion itself. It is a pity nobody has got to retort it into a valid particle, its singularity could had been used then to explain why only a small set of particles are actually observed (instead of needing multiple energy hierarchies).