I have an expression which has six terms. I am posting one of the terms, in its basic form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

f1= \int \frac{d\vec{k}}{( \xi [\vec{k}] + i d - \xi [\vec{k}-\vec{b}] ) ( \xi [\vec{k}] + i c + i d - \xi [\vec{k}-\vec{a} - \vec{b}]) }

[/tex]

Then there are f2, f3,f4..f6. They are all complex conjugates.

The six terms together constitute the expression [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex]. I am to integrate and hence evaluate and visualize the function [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex] in Mathematica. I was able to do the one-dimensional case correctly, where all the variables can be treated as scalars. However I am having trouble doing the 2-D case.

In fact, I am a little unsure about how the math works when vectors are involved, and also how to make mathematica evaluate this integration for me. Here is what I tried.

I declared

k={kx,ky} ... a={ax,ay} ... etc

The function [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex] now becomes a list as:

[tex] F(\vec{a},\vec{b},c,d,\vec{k}) = \{ F(ax,bx,c,d,kx) , F(ay,by,c,d,ky) \} [/tex]

Now if I use: Integrate[F, k]

I should expect an output of the form {Expr1,Expr2}

However, I get an error... "Integrate::ilim: Invalid integration variable or limit(s) in {kx,ky}."

Can somebody explain what I am doing wrong here?

Even more fundamentally, I somehow doubt if this approach to carrying out the integration is correct. Can someone hint how such integrations involving vector variables and complexes (iotas) are solved?

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# [Mathematica Help] An integration involving many vector variables

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