Hello, I am trying to prove that the momentum of an electromagnetic field is [tex]E \times B[/tex] by considering the conserved quantity due to the spatial translation of the Lagrangian.

[tex]L = - \frac{1}{4}\int {{F^{\mu v}}{F_{\mu v}}} {d^3}x[/tex]
So far, I have calculated the canonical momentum.
[tex]{\Pi _{{A_\mu }}} = \frac{{\partial {A_\mu }}}{{\partial t}} = \left( {\begin{array}{*{20}{c}}
0\\
{{E_x}}\\
{{E_y}}\\
{{E_z}}
\end{array}} \right)[/tex]

I know that the conserved quantity is
[tex]Q = \int {{\Pi _{{A_\mu }}}} \delta {A_\mu }{d^3}x[/tex]

But I am not sure how [tex]\delta {A_\mu }[/tex] is going to give me components of the curl.
Thank you very much.

[tex]L = - \frac{1}{4}\int {{F^{\mu v}}{F_{\mu v}}} {d^3}x[/tex]
So far, I have calculated the canonical momentum.
[tex]{\Pi _{{A_\mu }}} = \frac{{\partial {A_\mu }}}{{\partial t}} = \left( {\begin{array}{*{20}{c}}
0\\
{{E_x}}\\
{{E_y}}\\
{{E_z}}
\end{array}} \right)[/tex]

I know that the conserved quantity is
[tex]Q = \int {{\Pi _{{A_\mu }}}} \delta {A_\mu }{d^3}x[/tex]

But I am not sure how [tex]\delta {A_\mu }[/tex] is going to give me components of the curl.
Thank you very much.
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