hi, I try to use the Noether theorem to determinate the angular momentum of the electromagnetic field described by the Lagrangian density(adsbygoogle = window.adsbygoogle || []).push({});

L=-F^{αβ}F_{αβ}/4

After some calculation I find a charge J_{αβ}that is the angular momentum tensor. So the generator of rotations are

[itex](J^{23},J^{31},J^{12}) = \vec{J}[/itex]

and I find

[itex]\vec{J}[/itex] = [itex]\int d^{3}x ( \vec{E}\times \vec{A} + \sum _{k} E^{k} (\vec{x} \times \nabla ) A^{k} )[/itex]

Now I deduce that the field has an intrinsic angular momentum that is

[itex]\vec{S}[/itex] = [itex]\int d^{3}x ( \vec{E}\times \vec{A} ) [/itex]

but from this, once I quantized the field (for example in the Coulomb gauge, with the modified commutation relations) can I deduce something about the spin of the photon?

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# Electromagnetic spin from Noether theorem and spin photon

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