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From Jean Zinn-Justin:

"The conducting plates impose to the electric field to be perpendicular to the plates. It is easy to verify that this condition is satisfied if the vector field [itex]A_\mu[/itex] itself vanishes on the plates. Calling L the distance between the plates, z=0 and z=L the plate positions, we thus integrate over fields which have the fourier representation,

[tex]A_\mu (\mathbf{x}_{\perp},z)=\int d^{d-1}p_{\perp}\sum_{n\ge1} e^{ip_{\perp} \cdot \mathbf{x}_{\perp}} \sin(\pi z/L) \tilde{A}(\mathbf{p}_{\perp},n)[/tex],

where [itex]\mathbf{x_{\perp}}[/itex] are the space coordinates in the remaining directions."

OK so the bit that I dont understand is the fourier representation buisness. Am I right in thinking that the exponential factor is the imaginary part of the fields?

Also what is meant by [itex]\tilde{A}()[/itex]?

Answers to these questions or comments that will help to make this equation clear to me would be very much appreciated.

Thank you for your time.

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# Homework Help: Fourier representation of fields

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