- #1
zetafunction
- 391
- 0
why no change of variable to polar coordinates inside multi-loop integral ??
given a mul,ti-loop integral
[tex] \int d^{4}k_{1} \int d^{4}k_{2}....\int d^{4}k_{n}f(k_{1} , k_{2},...,k_{n}) [/tex]
which can be considered a 4n integral for integer n , my question is why can just this be evaluated by using a change of variable to 4n- polar coordinates ?
one we have made a change of variable and calculated the Jacobian, and integrated over ALL the angular variables we just have to make an integral
[tex] \int_{0}^{\infty}drg(r)r^{4n-1} [/tex] which is just easier to handle
given a mul,ti-loop integral
[tex] \int d^{4}k_{1} \int d^{4}k_{2}....\int d^{4}k_{n}f(k_{1} , k_{2},...,k_{n}) [/tex]
which can be considered a 4n integral for integer n , my question is why can just this be evaluated by using a change of variable to 4n- polar coordinates ?
one we have made a change of variable and calculated the Jacobian, and integrated over ALL the angular variables we just have to make an integral
[tex] \int_{0}^{\infty}drg(r)r^{4n-1} [/tex] which is just easier to handle