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I've a question. Where is the connection between the (kinetic) Lagrangian [tex] - \dfrac{1}{4} F_{\mu \nu} F^{\mu \nu} [/tex] and a plane wave of the form [tex] \vec{\varepsilon} exp(i \vec{k} \cdot \vec{x}) / \sqrt{V} [/tex] (the epsilon is a polarization vector) confined in a box with a finite volume V ? I should somehow "motivate" the factor [tex] - \dfrac{1}{4} [/tex] occurring in the Lagrangian by such plane waves. But I absolutely dont't have a clue how to do that. Does anyone have an idea? I hope somebody could help me.