- #1
muppet
- 602
- 1
Hi all,
I've reason to believe that the function
<br /> f(q)=\int\frac{d^{4+n} k}{(2\pi)^4}\frac{1}{(a \cdot k -i \epsilon) (b \cdot k -i \epsilon) (k^2 -i \epsilon) ((q-k)^2-i\epsilon)}<br />
where a, b are real -valued 4+n component vectors; epsilon is real, positive and infinitesmal, and taken to zero at the end of the calculation; and the dot denotes contraction of the vectors with the Minkowski bilinear form defined by Diag(-1,1,1,1), has two branch cuts. (As a physicist, I want to think of q and k as real (four+n)-component vectors as well, but I think it's necessary to extend these to allow to complex values.)
How can I go about finding out whether or not this is true? There's no obvious fractional exponents; my instinct is to switch to hyperspherical polars and see whether I get logarithms, but I'm thwarted by the fact that I have multiple dot products in the denominator, and don't know how to define the angles that would arise consistently.
Thanks in advance for your help.
I've reason to believe that the function
<br /> f(q)=\int\frac{d^{4+n} k}{(2\pi)^4}\frac{1}{(a \cdot k -i \epsilon) (b \cdot k -i \epsilon) (k^2 -i \epsilon) ((q-k)^2-i\epsilon)}<br />
where a, b are real -valued 4+n component vectors; epsilon is real, positive and infinitesmal, and taken to zero at the end of the calculation; and the dot denotes contraction of the vectors with the Minkowski bilinear form defined by Diag(-1,1,1,1), has two branch cuts. (As a physicist, I want to think of q and k as real (four+n)-component vectors as well, but I think it's necessary to extend these to allow to complex values.)
How can I go about finding out whether or not this is true? There's no obvious fractional exponents; my instinct is to switch to hyperspherical polars and see whether I get logarithms, but I'm thwarted by the fact that I have multiple dot products in the denominator, and don't know how to define the angles that would arise consistently.
Thanks in advance for your help.
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