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I'm trying to get a handle on my old Nemesis, Green functions. I have a massless scalar field confined between two parallel plates separated by a distance a (in the z dimension) and the field satisfies Dirichel BC's. Basically I'm trying to work from line 1 of a book to line 2 (K. Miltons the Casimir Effect p23).

'The Green function satisfies'

[tex]-\partial^2G(x,x')=\delta(x-x')[/tex]

"We introduce a reduced Green function g(z,z) according to the Fourier Transform"

[tex]G(x,x')=\int\frac{d^dk}{(2\pi)^d}e^{i\vec{k}.(x-x')}\int\frac{d\omega}{2\pi}e^{-i\omega(t-t')}g(z,z') [/tex]

This is all the book says so sorry of thats not much info. I'm fairly sure that [tex]\partial=\nabla+\frac{d}{dt}[/tex].

What I want to understand (and see the math for) is how to get from line 1 to line 2. I'm pretty sure that it involves fourier transforms, but I would like to see it. Also, I don't understand the concept of a reduced green function. Can anyone either point me to a good reference, or better still explain how and why it is used.

I hope someone can walk me through this.

:)

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# Green Functions and BC's

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