
October 20th, 2006, 08:31 PM
#1
Senior Member
Any Math wizards here?
Long story short, I decided to go to get more education (grad school) as a physicist. However, my focus is quantum gravity (always fun stuff when the adjective quantum is being used ) and I need to learn qualitative mathematics.
So my problem is I need to learn qualitative math but I don't have a clue where to begin! I have been told "Topos theory" and "Category theory" are a "good start", but frankly I would like to verify this with a math wizard...someone with experience or knowledge of these things.
Any help would be greatly appreciated!
"The Texan turned out to be goodnatured, generous and likeable. In three days no one could stand him." Catch 22 by Joseph Heller.
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December 10th, 2006, 07:45 AM
#2
Senior Member
Goto a local university, ask the professor of quantum mechanics.

December 10th, 2006, 10:41 AM
#3
Hi
Good knowledge of differential geometry[1], differential topology[1] and
functional analysis[2] is mandatory if you want to understand anything
involving the word quantum
These mathematical fundamentals will allow you to understand quantum
states and quantum operators  whether they are welldefined, not welldefined  and which are hoped to be welldefined ...
These fundamentals will also allow you to understand curvatures of spaces,
which are extremely important for general relativity (e.g. Ricci tensors).
They will also help you to understand statistical mechanics  a topic
extremely important to understand mechanism in the evolution of the
universe (expansion, cooling down, phase transitions, ...).
Good luck!
Cheers.
[1] http://en.wikipedia.org/wiki/Differe...y_and_topology
[2] http://en.wikipedia.org/wiki/Functional_analysis
Last edited by sec_ware; December 10th, 2006 at 10:44 AM.
If the only tool you have is a hammer, you tend to see every problem as a nail.
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December 14th, 2006, 07:40 AM
#4
Junior Member
Hey will u first explain me this "quantum". Wats this all about? I got my first college course on the topic earlier this year, but frankly speaking I got none of it into my head. So plzzz tell me wat fascinates u,Arkimedes? btw gud name! lol
partyhardworkHARDER

January 2nd, 2007, 06:10 PM
#5
Senior Member
Well, first of all, I'm sorry I haven't replied since I started this thread. I am at school, and I've been swamped with work.
Thanks sec_ware, but I am interested in foundational problems of quantum mechanics (basically answering the question "Why is quantum mechanics so ****ed up?"). I've been reading Relational quantum mechanics by Carlo Rovelli, Geometry of Quantum Mechanics by J.M. Isidro, and a few other papers directed towards answering this question.
I've been consulting the local quantum gravity guru on his opinion, and I think I've been pointed to an interesting direction. Take topos (categorical logic a sort of insanely obscure modal logic) and apply it to relational quantum mechanics.
"The Texan turned out to be goodnatured, generous and likeable. In three days no one could stand him." Catch 22 by Joseph Heller.
Buddies? I have no buddies...
Give the BSD daemon some love (proud FreeBSD user)
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