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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 m-th 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 D-1.
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} ((x-y)^m(x-y)^n+(y-z)^m(y-z)^n+(z-x)^m(z-x)^n) + I T_{mn} ((y-x)^m(z-x)^n+(z-y)^m(x-y)^n+(x-z)^m(y-z)^n)}

b is a positive real constant. G_{mn} is a positive-definite 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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