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Hamiltonian density of EM fields
I'm learning about the field theory of electromagnetism. The Lagrangian density for an electromagnetic field can be taken to be$$\mathcal{L} = -\frac{1}{4} F^{\mu\nu} F_{\mu\nu} + \mu_0 A^\mu...
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The metric convention is (-+++). Given the Lagrangian, the conjugate momenta are defined as\begin{align*} \pi^j = \frac{\partial \mathcal{L}}{\partial (\partial_0 A_j)} = F^{j0} =...
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