Quantum Gravity Seminar - Fall 2004, Week 3 [Archive]

John Baez

Apr20-05, 06:23 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>\nIn the 2004-2005 academic year, the Quantum Gravity Seminar\nat UCR is about gauge theory and topology. Derek Wise took\nnotes of my lectures.\n\nIn week 3:\n\nhttp://math.ucr.edu/home/baez/qg-fall2004/f04week03.pdf\n\nwe continued our history of categories and physics from the\nPonzano-Regge model of 3d quantum gravity, to Grothendieck\'s\ndreams about infinity-categories, to the rise of string theory\nin the 1980s.\n\nPonzano and Regge actually did their work before Penrose\ninvented spin networks, and they published their work in\nthe proceedings of a conference on spectroscopy! But,\nit\'s much easier to understand if you already know about\nspin networks, so I\'ve reversed the flow of events here.\nThink of it as a little quantum fluctuation.\n\nA more detailed version of this history, still in draft form,\ncan be found in pages 18-22 of this paper:\n\nA History of n-Categorical Physics\nhttp://math.ucr.edu/home/baez/qg-winter2005/history.pdf\n\nNotes from the whole fall quarter can be found here:\n\nhttp://math.ucr.edu/home/baez/qg-fall2004/\n\nNotes from other sessions of the Quantum Gravity Seminar\nare here:\n\nhttp://math.ucr.edu/home/baez/QG.html\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 the 2004-2005 academic year, the Quantum Gravity Seminar
at UCR is about gauge theory and topology. Derek Wise took
notes of my lectures.

In week 3:

http://math.ucr.edu/home/baez/qg-fall2004/f04week03.pdf

we continued our history of categories and physics from the
Ponzano-Regge model of 3d quantum gravity, to Grothendieck's
dreams about infinity-categories, to the rise of string theory
in the 1980s.

Ponzano and Regge actually did their work before Penrose
invented spin networks, and they published their work in
the proceedings of a conference on spectroscopy! But,
it's much easier to understand if you already know about
spin networks, so I've reversed the flow of events here.
Think of it as a little quantum fluctuation.

A more detailed version of this history, still in draft form,
can be found in pages 18-22 of this paper:

A History of n-Categorical Physics
http://math.ucr.edu/home/baez/qg-winter2005/history.pdf

Notes from the whole fall quarter can be found here:

http://math.ucr.edu/home/baez/qg-fall2004/

Notes from other sessions of the Quantum Gravity Seminar
are here:

http://math.ucr.edu/home/baez/QG.html

John Baez

Oct11-06, 02:41 PM

In the 2004-2005 academic year, the Quantum Gravity Seminar
at UCR is about gauge theory and topology. Derek Wise is
taking notes on my lectures.

In week 4:

http://math.ucr.edu/home/baez/qg-fall2004/f04week04.pdf

we continued our history of categories and physics into the
late 1980s, when strings and loops met categories. We
discuss Graeme Segal's definition of "conformal field theory",
Atiyah's definition of "topological quantum field theory",
and Joyal and Street's definition of "braided monoidal category".

At this point the interaction between category theory and physics
becomes so strong that we must leave out everything except some
key highlights.

A more detailed version of this history, still in draft form,
can be found in pages 22-23 of this paper:

A History of n-Categorical Physics
http://math.ucr.edu/home/baez/qg-winter2005/history.pdf

There was a homework assignment on "Connections as Functors",
which shows that in gauge theory, the map assigning to any
path its "parallel transport" is a functor:

http://math.ucr.edu/home/baez/qg-fall2004/connection.pdf

Together with the previous assignment on "Action as a Functor",
one should get the idea that a Lagrangian is a kind of connection -
and it's true! This fact is most striking for electromagnetism,
since both connections involve the gauge group U(1).

You can see answers by Jeffrey Morton, Derek Wise, Toby
Bartels and Prasad Senesi:

http://math.ucr.edu/home/baez/qg-fall2004/connection_jeffrey.pdf
http://math.ucr.edu/home/baez/qg-fall2004/connection_derek.pdf
http://math.ucr.edu/home/baez/qg-fall2004/connection_toby.pdf
http://math.ucr.edu/home/baez/qg-fall2004/connection_prasad.pdf

Notes from the whole fall quarter can be found here:

http://math.ucr.edu/home/baez/qg-fall2004/

Notes from other sessions of the Quantum Gravity Seminar
are here:

http://math.ucr.edu/home/baez/QG.html