There is a lot. For instance, see topics on general theory of relativity http://www.physicsoftheuniverse.com/topics_relativity_general.html
Dear Esakki,
the crystalline state is a very nice example of the strong relation between physics and geometry. Atoms, molecules, ions during the crystallization are subjected to severe constraints (geometrical, of course). As a matter of fact, they are obliged to follow symmetry rules ( symmetry planes, symmetry axes, inversion centres) giveng rise to a limited number , 32, of point groups (morphological symmetry) and space groups , 230, (structural symmetry.
All the best
Dino
If you are interested in education, then this article might be of interest:
Hanna, G., & Jahnke, H. N. (2002). Arguments from physics in mathematical proofs: An educational perspective. For the learning of mathematics, 38-45.
http://flm-journal.org/Articles/2BC6E1FE087FB203321F3E938B905F.pdf
In classical mechanics you have phase space, in rel. mechanics Minkowsky space, in quantum mechanics you have Hilbert space, in strings you have toroidal space, in general relativity you have (eventually) Riemannian space, and in mathematical physics you have function spaces. All these spaces may have different metrik, norm and scalar product (invariant bilinear forms) and are so far topologically (very) different.
I would like coming back to the example I proposed. I tried to explain that , in the case of crystals, the physical properties related to the crystalline field (order, periodicity) generated the geometrical characteristics that we observe ( polyhedral 3D objects, lattice point symmetries...). Don't forget that Hauy, who discovered the main rule of the crystallography, started from the observation of geometrical properties and hence deduced (first in the history of the human being) the physical property of discontinuity in the solid state.
Thanks for your kind attention
Dino
Thank you for all your answers. I did PhD in pure maths. I would like to work on Quantum gravity. Can I apply for another PhD for physics?. Pls guide me.
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