I do not know what "division of physics" specifically refers to. If you are looking for the axiomatization of physics (one of Hilbert's problems), read the article below:
http://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem
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There is no quantum physics of a moose. Quantum physics is a type of theoretical physics, and its laws do not apply to physical objects
Of all the sciences, physics is very demanding for maths. So if you are really strong at maths, physics might just be for you
It really depends. If you are good at understanding the concepts of math and you think you can grasp the concepts of physics (which is not bad at all), then you will do fine in physics. Physics is like 50% math 50% concepts. This is my second year of physics (I am doing Physics with Calculus now) and it really isn't as bad as most people think.
5 branches of physics
Mathematics is the Microscope and Telescope and Language of Physics.