| Topic: |
Science > Physics |
| User: |
"John Baez" |
| Date: |
12 Apr 2005 12:15:44 AM |
| Object: |
Quantum Gravity Seminar - Fall 2004, Week 1 |
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 1:
http://math.ucr.edu/home/baez/qg-fall2004/f04week01.pdf
we continued our history of categories and physics from Born's
"probability interpretation" of Heisenberg's matrix mechanics,
to Feynman path integrals and Feynman diagrams. In retrospect,
expressing time evolution
exp(-itH)
as a limit of the nth power of the matrix (1 - itH/n) quickly
leads to Feynman path integrals.
We then quickly sketch Eilenberg and Mac Lane's basic work on
category theory. The climax of this episode came with Mac Lane's
discovery of monoidal and symmetric monoidal categories. These
were later seen to be the proper framework for understanding
Feynman diagrams and their diverse generalizations, from electrical
circuit diagrams to proof nets in logic.
A more detailed version of this history, still in draft form,
can be found in pages 6-13 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 "Groups as Categories",
which begins to explain how categories generalize groups as
a framework for understanding symmetry:
http://math.ucr.edu/home/baez/qg-fall2004/categories1.pdf
You can see answers by Toby Bartels, Jeffrey Morton, Derek
Wise and Miguel Carrion Alvarez:
http://math.ucr.edu/home/baez/qg-fall2004/categories1_toby.pdf
http://math.ucr.edu/home/baez/qg-fall2004/categories1_jeffrey.pdf
http://math.ucr.edu/home/baez/qg-fall2004/categories1_derek.pdf
http://math.ucr.edu/home/baez/qg-fall2004/categories1_miguel.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
.
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