Category Theory and Physics

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klw1026@gmail.com - 17 Feb 2008 09:54 GMT

I am currently working my way through classical Yang-Mills theory with
the help of John Baez's book on gauge fields and some others. I have
recently just began to notice the new, well new to myself, research on
higher gauge theory. This looks very interesting but I feel that my
background in category theory is too weak to actually understand
everything that is going on. This seems to be a recurring theme as I
try to advance my knowledge of mathematical physics. Last semester I
took a course on topological quantum field theory and another on
quantum groups and I feel that I did not get a lot out of it due to
the amount of category theory that was used. So my question is this:
does anyone know of a good reference for learning category theory? I
have looked at Mac Lane's book but find a bit "spooky" with the amount
of set theory he uses. Thanks for the help.

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Igor Khavkine - 19 Feb 2008 04:04 GMT

> I am currently working my way through classical Yang-Mills theory with
> the help of John Baez's book on gauge fields and some others. I have
[quoted text clipped - 9 lines]
> have looked at Mac Lane's book but find a bit "spooky" with the amount
> of set theory he uses. Thanks for the help.

John himself is fond of talking about category theory and its relation
to physics. So, not a bad place to start would be his own website. See
for instance [1] and [2]. The notes from his website are often presented
in a very casual manner, so to get the most out of them you might want
to followup on his references while working through them.

[1] http://math.ucr.edu/home/baez/categories.html
[2] http://math.ucr.edu/home/baez/QG.html

Hope this helps.

Igor

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Lou Pecora - 20 Feb 2008 09:37 GMT

> John himself is fond of talking about category theory and its relation
> to physics. So, not a bad place to start would be his own website. See
[quoted text clipped - 8 lines]
>
> Igor

I've just been lurking a little on this thread, but I looked at these
web pages and I would recommend them, too. Very nice intro to
Categories. And I started knowing nothing about categories. The
explanation of the lack of a functor from classical systems to quantum
systems that would represent a quantization was enlightening since it
also showed a good example of functors and categories and the
application.

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-- Lou Pecora

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Natural Science Forum / Physics / Research / February 2008

Category Theory and Physics