Author 
Comment/Response 
Xyen

04/28/11 12:47pm
I need to calculate the integral over an exponential function with a tensor product.
It is basically T_{mn} x^m y^n . "x^m" is NOT x to the power of m! The subscript "_{mn}" and superscripts "^n" are all INDICES denoting the components, so "x^m" is the mth component of the vector x. So, T_{mn} x^m y^n is the tensor product of T with x and y.
The number of components is not fixed but same, let's call it "D":
m and n go from 0 to D1.
D means the number of space dimensions.
What I need to calculate is the integral
{\int_{\infty}^{\infty}}^3 dx dy dz e^{ b G_{mn} ((xy)^m(xy)^n+(yz)^m(yz)^n+(zx)^m(zx)^n) + I T_{mn} ((yx)^m(zx)^n+(zy)^m(xy)^n+(xz)^m(yz)^n)}
b is a positive real constant. G_{mn} is a positivedefinite symmetric tensor. T_{mn} is an antysymmetric tensor. I is the imaginary unit. e is the exponential function. x,y,z are vectors.
The integration is run three times subsequently over x, y and z each from minus infinity to plus infinity.
How can this calculation be input in Mathematica?
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