- #1
paolorossi
- 24
- 0
hi, I try to use the Noether theorem to determinate the angular momentum of the electromagnetic field described by the Lagrangian density
L=-FαβFαβ/4
After some calculation I find a charge Jαβ 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?
L=-FαβFαβ/4
After some calculation I find a charge Jαβ 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?