Will studying fourier analysis prepare one for string theory and QP?

[strings235]

hey does anyone know if studying Fourier analysis is going to aid in physics, particularly in string theory or quantum physics?

 

[CompuChip]

Yes it is.

Just one quick example: often physicists have to solve differential equations, like $$\mathcal{L}\phi = f$$ for given $$f$$ and differential operator $$\mathcal{L}$$. One way do do this is by constructing a Greens function which satisfies $$\mathcal{L}G(x) = \delta(x)$$ (that's a Dirac delta) and then the equation can be solved for any $$f$$ by convolution; $$\phi = G * f = \int G(x - x') f(x') dx'$$. Once you do this for different differential operators, you'll notice that it's often much handier to solve the Fourier components of $$G$$ separately (especially since the delta function has such an easy Fourier transform) and then back-transform them to get G.

In fact, I have heard that in field theories (QFT, for example) people love working in Fourier space, as problems are often relatively simple there and a real pain in the neck to do in real space.

So my advise would be: if you can study Fourier analysis, do it.

 

[strings235]

and would you recommend I study applied or theoretical mathematics if i were to do a double major with physics? thanks for the post btw.

 

[Reverie]

and would you recommend I study applied or theoretical mathematics if i were to do a double major with physics? thanks for the post btw.

I would recommend studying theoretical mathematics. Differential Geometry and Functional Analysis would be quite useful. Fourier Analysis is also quite useful. Many, many things are quite useful...

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