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

  • Thread starter strings235
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hey does anyone know if studying fourier analysis is going to aid in physics, particularly in string theory or quantum physics?
 

CompuChip

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Yes it is.

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

[tex]E=mc^{2}[/tex] :rofl:
 

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