<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>\nHave there ever been any major objections to field theories based upon\nnon-associative bases, such as the octonions?\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>Have there ever been any major objections to field theories based upon
non-associative bases, such as the octonions?
Raoul E. Cawagas
Aug23-04, 04:06 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>\n\nthoovler@excite.com (Igor) wrote in message news:<d434b6c6.0408190343.350cb42f@posting.google. com>...\n> Have there ever been any major objections to field theories based upon\n> non-associative bases, such as the octonions?\n\nTo my knowledge, no "major" objections have so far been presented on\nfield theories based on non-assciative algebras. In fact a lot of work\nis now being done on the use of octonions and other Cayley-Dickson\n(C-D) algebras in theoretical physics. Even the sedenions (the C-D\ndouble of the octonions) is now being seriously considered for\npotential applications in elementary particle physics. John Baez has\nwritten a monograph on the octonions which you might find interestng.\n\nRaoul E. Cawagas\nSciTech R&D Center\nPolytechnic University of the Philippines\nSta. Mesa, Manila\nE-mail: raoulec@yahoo.com\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>thoovler@excite.com (Igor) wrote in message news:<d434b6c6.0408190343.350cb42f@posting.google.com>...
> Have there ever been any major objections to field theories based upon
> non-associative bases, such as the octonions?
To my knowledge, no "major" objections have so far been presented on
field theories based on non-assciative algebras. In fact a lot of work
is now being done on the use of octonions and other Cayley-Dickson
(C-D) algebras in theoretical physics. Even the sedenions (the C-D
double of the octonions) is now being seriously considered for
potential applications in elementary particle physics. John Baez has
written a monograph on the octonions which you might find interestng.
Raoul E. Cawagas
SciTech R&D Center
Polytechnic University of the Philippines
Sta. Mesa, Manila
E-mail: raoulec@yahoo.com
John Baez
Aug23-04, 08:36 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>\nIn article <95639de8.0408201530.4ee9f95d@posting.google.com>, \nRaoul E. Cawagas <raoulec@yahoo.com> wrote:\n\n>thoovler@excite.com (Igor) wrote in message\n>news:<d434b6c6.0408190343.350cb42f@posti ng.google.com>...\n\n>> Have there ever been any major objections to field theories based upon\n>> non-associative bases, such as the octonions?\n>\n>To my knowledge, no "major" objections have so far been presented on\n>field theories based on non-assciative algebras. In fact a lot of work\n>is now being done on the use of octonions and other Cayley-Dickson\n>(C-D) algebras in theoretical physics. Even the sedenions (the C-D\n>double of the octonions) is now being seriously considered for\n>potential applications in elementary particle physics. John Baez has\n>written a monograph on the octonions which you might find interestng.\n\nIt\'s not really a monograph, just an article:\n\nThe Octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205,\nalso available at http://ww.arxiv.org/abs/math.RA/0105155\nand with additional material at http://math.ucr.edu/home/baez/Octonions/\n\nThe version on my website includes a new review of Conway and Smith\'s\nbook "On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry":\n\nhttp://math.ucr.edu/home/baez/Octonions/conway_smith/\n\nThe octonions show up in many contexts in superstring theory, but\nfew would say this theory is "based" on the octonions. A better\ndescription might be that string theorists are forced into using special\nalgebraic structures to get things to work, and these special structures\nhave an unnerving habit of being related to the octonions. Of course,\nthis is far more interesting than if they\'d *set out* to incorporate\nthe octonions into their work.\n\nGeoffrey Dixon has an extension of the Standard Model which makes\nuse of all four normed division algebras: reals, complexes, quaternions\nand octonions:\n\nGeoffrey M. Dixon, Division Algebras: Octonions, Quaternions,\nComplex Numbers and the Algebraic Design of Physics, Kluwer, Dordrecht, 1994.\n\nNot enough people have looked at this stuff carefully, but if one does,\none finds interesting relations to the SU(5) and SO(10) grand\nunified theories, which show how the patterns underlying the symmetry\nbreaking in these theories are related to division algebras. Sometime\nI\'d like to write about this. You can read more about Dixon\'s ideas here:\n\nhttp://www.7stones.com/Homepage/AlgebraSite/algebra0.html\n\nThere is also a bit more lurking in my seminar notes on Clifford\nalgebras, spinors, the Standard Model and the SU(5) grand unified\ntheory:\n\nhttp://www.math.ucr.edu/home/baez/qg-spring2003/\n\nthough I didn\'t manage to cover enough of the really cool stuff.\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"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <95639de8.0408201530.4ee9f95d@posting.google.com>,
Raoul E. Cawagas <raoulec@yahoo.com> wrote:
>thoovler@excite.com (Igor) wrote in message
>news:<d434b6c6.0408190343.350cb42f@posting.google.com>...
>> Have there ever been any major objections to field theories based upon
>> non-associative bases, such as the octonions?
>
>To my knowledge, no "major" objections have so far been presented on
>field theories based on non-assciative algebras. In fact a lot of work
>is now being done on the use of octonions and other Cayley-Dickson
>(C-D) algebras in theoretical physics. Even the sedenions (the C-D
>double of the octonions) is now being seriously considered for
>potential applications in elementary particle physics. John Baez has
>written a monograph on the octonions which you might find interestng.
It's not really a monograph, just an article:
The Octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205,
also available at http://ww.arxiv.org/abs/math.RA/0105155
and with additional material at http://math.ucr.edu/home/baez/Octonions/
The version on my website includes a new review of Conway and Smith's
book "On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry":
http://math.ucr.edu/home/baez/Octonions/conway_smith/
The octonions show up in many contexts in superstring theory, but
few would say this theory is "based" on the octonions. A better
description might be that string theorists are forced into using special
algebraic structures to get things to work, and these special structures
have an unnerving habit of being related to the octonions. Of course,
this is far more interesting than if they'd *set out* to incorporate
the octonions into their work.
Geoffrey Dixon has an extension of the Standard Model which makes
use of all four normed division algebras: reals, complexes, quaternions
and octonions:
Geoffrey M. Dixon, Division Algebras: Octonions, Quaternions,
Complex Numbers and the Algebraic Design of Physics, Kluwer, Dordrecht, 1994.
Not enough people have looked at this stuff carefully, but if one does,
one finds interesting relations to the SU(5) and SO(10) grand
unified theories, which show how the patterns underlying the symmetry
breaking in these theories are related to division algebras. Sometime
I'd like to write about this. You can read more about Dixon's ideas here:
http://www.7stones.com/Homepage/AlgebraSite/algebra0.html
There is also a bit more lurking in my seminar notes on Clifford
algebras, spinors, the Standard Model and the SU(5) grand unified
theory:
http://www.math.ucr.edu/home/baez/qg-spring2003/
though I didn't manage to cover enough of the really cool stuff.
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