What Are the Key Connections Between Math and Physics in Mathematical Physics?

[andyroo]

Some people call it physics that simply is more difficult or reliant on mathematics. I was wondering if anyone could enlighten me a bit more as to what types of maths and physics areas are generally equated with mathematical physics.

 

[MathematicalPhysicist]

I think it's more of a buzzword than anything else.

If you are researching in the mathematics of a physical theory then your'e doing math, if you use math to build a physical theory than your'e doing theoretical physics.

 

[Fredrik]

For example, the people who built up the whole machinery of quantum field theories and figured out how to use it to make predictions about results of experiments were theoretical physicists. The people who try to find exact definitions of such terms as "quantum field" and "path integral", which can be used to rigorously prove the results of theoretical physics (and perhaps some new results as well), are mathematical physicists. (There is still no rigorous version of quantum electrodynamics on ℝ⁴).

Theoretical physicists can sometimes get away with just barely knowing what a Hilbert space is, while mathematical physicists need to know a ****load of functional analysis and other difficult math (in particular topology and differential geometry).

 

[andyroo]

Thanks for giving me such great examples!