Physics & Topology: Research, Books & Articles

[rushil]

One day, I decided to find out in which places topics in Mathematics and Physics were interlinked or used to prove results in each other's topics. Most of Mathematics is applied everywhere in Physics - from Calculus to Group Theory etc. I considered that possibly the only field which is not talked much about is the application of Topology to Physics and vice-versa. So what do you think about this? What are the possibilities for research? What has been done? Do you have any books or online articles to recommend??
Also, do you have any other possible topics in interconnection of Physics and Mathematics that are interesting??

 

[robphy]

http://arxiv.org/abs/hep-th/9709135
Topology and physics-a historical essay - C. Nash

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Knots_and_physics.html

http://www.iop.org/EJ/abstract/0034-4885/33/2/303
Group theory and topology in solid state physics
J Killingbeck 1970 Rep. Prog. Phys. 33 533-644

http://physics.harvard.edu/~dtlarson/tutorial05/
How to Talk to a Physicist: Groups, Symmetry, and Topology
Daniel Larson

http://arxiv.org/abs/hep-th/9109030
Topology Change in General Relativity
Gary T. Horowitz

http://www.citeulike.org/user/mukundn/article/416002
On the mathematical foundations of electrical circuit theory
Smale S - J. Differential Geometry, Vol. 7 (1972), pp. 193-210.

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Eugene Wigner

 

[dextercioby]

Since Topology is the basis for Functional Analysis and Differential Geometry, i'd say all physics is refined, applied topology...

Daniel.

 

[fourier jr]

when applied to function spaces, ascoli's theorem allows the existence of many differential equations (which i guess come from physics, or have physical applications). ascoli's theorem needs tychonoff's product theorem (the product of compact spaces is compact) in its proof.

 

[matt grime]

Look at Jon Baez's famous 'This Week's finds in Mathematical Physics'

There are also applications of algebra to stochastical mechanics in very surprising ways.

Then there is string theory which is almost entirely mathematical. For instance a (topological) QFT is a functor from the Segal's category of Riemann Surfaces to Vect.

Virasoro (Spelling anyone?) algebras, lattice operators and monster groups, quantum groups, integrable systems, symplectic manifolds, representations of Lie algebras as integral aspects of particle physics, erm, and many things I've never heard of.