A quesiton about multidimensional Fourier transform

[zetafunction]

my question is the following

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

here $$p^{2}= p_{0}^{2}+p_{1}^{2}+p_{2}^{2}+p_{3}^{2}$$

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

for the scalar product i can use the definition $$p*k= |p|.|k|.cos(u)$$

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

 

[mathman]

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 ∞.