A quesiton about multidimensional Fourier transform

  • #1
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0

Main Question or Discussion Point

my question is the following

let be the Fourier transform [tex] \int_{-\infty}^{\infty}d^{4}p \frac{exp( ip*k)}{p^{2}+a^{2}} [/tex]

here [tex] p^{2}= p_{0}^{2}+p_{1}^{2}+p_{2}^{2}+p_{3}^{2} [/tex]

is the modulus of vector 'p' , here * means scalar product

for the scalar product i can use the definition [tex] p*k= |p|.|k|.cos(u) [/tex]

so ony the modulus appear, my quesiton is if there is a way to set cos(u) =1 to get rid of the integration about angular variables, thanks
 

Answers and Replies

  • #2
mathman
Science Advisor
7,797
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There is (I don't know the form offhand) a 4 dimensional analog to spherical coordinates. Let p be the magnitude of (p1,p2,p3,p4). The differential will look like p3dpdA where A is the 4-d analog of surface area of the unit sphere. The A integral is over the 4-d unit sphere - includes the cos(u) factor. The p integral is from 0 to ∞.
 

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