View Full Version : Chern-Simons theory challenge
<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>In 1993, the then UK Science Minister, William\nWaldegrave, issued a challenge to physicists to answer\nthe questions \'What is the Higgs boson, and why do we\nwant to find it?\' on one side of a single sheet of\npaper. (http://hepwww.ph.qmw.ac.uk/epp/higgs.html)\n\nIn November 2000, "Institutional Investor Magazine"\nasked James Simons to explain Chern-Simons theory.\nAfter half an hour, he allowed "I can\'t".\n(http://www.charttricks.com/Resources/Articles/jim_simons.pdf)\n\nWhat could be a "popular science" description of\nChern-Simons theory?\n\n\n\n\n\n_______________________________ _______________________\nYahoo! for Good\nDonate to the Hurricane Katrina relief effort.\nhttp://store.yahoo.com/redcross-donate3/\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 1993, the then UK Science Minister, William
Waldegrave, issued a challenge to physicists to answer
the questions 'What is the Higgs boson, and why do we
want to find it?' on one side of a single sheet of
paper. (http://hepwww.ph.qmw.ac.uk/epp/higgs.html)
In November 2000, "Institutional Investor Magazine"
asked James Simons to explain Chern-Simons theory.
After half an hour, he allowed "I can't".
(http://www.charttricks.com/Resources/Articles/jim_simons.pdf)
What could be a "popular science" description of
Chern-Simons theory?
__{_______________________________________________ _____}
Yahoo! for Good
Donate to the Hurricane Katrina relief effort.
http://store.yahoo.com/redcross-donate3/
Daniel Moskovich
Sep15-05, 09:03 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>It isn\'t exactly a popular science description but it can easily be\ndumbed down to one- the first section of:\nThe Århus integral of rational homology 3-spheres I: A highly non\ntrivial flat connection on S3 by Dror Bar-Natan, Stavros Garoufalidis,\nLev Rozansky and Dylan P. Thurston\narXiv:q-alg/9706004.\nPush the "pretend you have a non-trivial flat connection" argument-\nexplain assuming implicitly that it exists, and then admitting that it\ndoesn\'t exist, and therefore one must use Feynman integrals.\nConnections can be pop-science explained as an "index" like the\n"Dow-Jones Index" which makes sense for financially-minded listeners.\nBar-Natan TEACHES differential topology this way- he explains financial\nindexes and then says "in math/phys these are called connections".\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>It isn't exactly a popular science description but it can easily be
dumbed down to one- the first section of:
The Århus integral of rational homology 3-spheres I: A highly non
trivial flat connection on S3 by Dror Bar-Natan, Stavros Garoufalidis,
Lev Rozansky and Dylan P. Thurston
arXiv:q-alg/9706004.
Push the "pretend you have a non-trivial flat connection" argument-
explain assuming implicitly that it exists, and then admitting that it
doesn't exist, and therefore one must use Feynman integrals.
Connections can be pop-science explained as an "index" like the
"Dow-Jones Index" which makes sense for financially-minded listeners.
Bar-Natan TEACHES differential topology this way- he explains financial
indexes and then says "in math/phys these are called connections".
vantuyll@gmail.com
Sep19-05, 04:54 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>An example of exceptionally good pop science:\nhttp://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf\n\n\nAn attempt to start a pop science explanation of Chern-Simons theory:\n\nEvery point in space-time has a copy of a vector space, called a fiber\nbundle; the fibers are the vector spaces. The vectors in these internal\nspaces, spread out over real space, are the matter field. The\nconnection specifies how to compare vectors attached to different\npoints (by parallel transport). If, when you move along a closed path,\nthe vector you start with is different from the one you end with, then\nthe connection is curved. Both fields, matter and connection (also\ncalled gauge field), vary over time, obeying a principle of least\naction.\n\nChern-Simons theory is a topological gauge theory in three dimensions\nwhich describes knot and three-manifold invariants. There is a\ncorrespondence to topological string theory, which is related to\nGromov-Witten invariants.\n\nReferences:\nA Unified Grand Tour of Theoretical Physics, Ian Lawrie\nChern-simons Theory, Matrix Models, And Topological Strings, Marcos\nMarino\n\n\nAn answer to Daniel:\n\nAsset price bundles are vectors in asset space. Calculating net present\nvalues is parallel transporting these vectors along a connection. The\nconnection includes prices and discounting as its spatial and temporal\nelements. Curvature is excess return.\n\nReference:\nPhysics of Finance, Kirill Ilinski\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>An example of exceptionally good pop science:
http://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf
An attempt to start a pop science explanation of Chern-Simons theory:
Every point in space-time has a copy of a vector space, called a fiber
bundle; the fibers are the vector spaces. The vectors in these internal
spaces, spread out over real space, are the matter field. The
connection specifies how to compare vectors attached to different
points (by parallel transport). If, when you move along a closed path,
the vector you start with is different from the one you end with, then
the connection is curved. Both fields, matter and connection (also
called gauge field), vary over time, obeying a principle of least
action.
Chern-Simons theory is a topological gauge theory in three dimensions
which describes knot and three-manifold invariants. There is a
correspondence to topological string theory, which is related to
Gromov-Witten invariants.
References:
A Unified Grand Tour of Theoretical Physics, Ian Lawrie
Chern-simons Theory, Matrix Models, And Topological Strings, Marcos
Marino
An answer to Daniel:
Asset price bundles are vectors in asset space. Calculating net present
values is parallel transporting these vectors along a connection. The
connection includes prices and discounting as its spatial and temporal
elements. Curvature is excess return.
Reference:
Physics of Finance, Kirill Ilinski
vBulletin® v3.8.7, Copyright ©2000-2012, vBulletin Solutions, Inc.