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I'm starting with the Lagrangian of a massive scalar field and have found an expression for the expectation value of the energy-momentum tensor.

[tex]<T_{\mu \nu}>=(\partial_\mu \partial_\nu-\frac{1}{2}(g_{\mu \nu}(\partial_\mu \partial_\nu+m^2))G(x-x')[/tex]

let say I have some Green Function G(x-x') and then I compactify the dimension into a circle or radius R, then can someone explain why we write the GF as:

[tex]G(x-x')=\sum_{n=1}^\infty G_\infty(x-x'+2\pi R n \hat{y})[/tex]

And explain the phrase: the Casimir energy can be easily obtained by summing over the infinite volume Green Function over all the images.

What are the images here?

Any help appreciated!!

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# Higher Dimensional Green Function

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