# Is there orbital angular momentum for all particles?

Light as an electromagnetic wave can be polarized in different ways, e.g. linear or circular. As far as I understand it currently this can be compared to the spin direction of a propagation electron (spin angular momentum of light). Now I have learned that an electromagnetic wave can also have an orbital angular momentum, which is described for example in Wikipedia as a kind of shifted wavefront. While trying to get my head around these phenomena I was thinking about other wave-like objects in physics besides photons.

Do all particles and/or excitations (e.g. a spin wave) exhibit orbital angular momentum and what are the physical consequences?

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In the very wikipedia link that you posted about the orbital angular momentum of light, there is reference to a paper by Belifante which answers your question for arbitraty fields. –  Vijay Murthy Mar 5 '12 at 14:16
Aren't orbital angular momentum just quantum analog of classical angular momentum? Then all should have it. –  Siyuan Ren Mar 5 '12 at 14:16

Yes. All particles (and excitations) can have angular momentum.

At the quantum level of description you are dealing with wavefunction for a given particle (or excitation). And the basic logic behind the orbital angular momentum for light is transferred to the OAM for wavefunctions. Its intuitive description can similarly be done in terms of the "shifted wavefronts".

The basic physical consequence is, of course, the usual conservation of the angular momentum. If your system is rotation invariant, then the total momentum (and its projection on some selected axis) of it should be constant.

Another more subtle consequence is the selection rules: by studying how your momenta couple to each other, you can make some statements about relative importance of different transitions between quantum states of your system.

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I'd do some math for such a generous bounty. But I'm not sure at which topic and which level should I concentrate... –  Kostya Mar 6 '12 at 16:03
Thank you for your offer Kostya. I am not sure whether I can formalize my current understanding much better. The question originated from an article where the orbital angular momentum was used to modulate an EM wave instead of the normal polarization. My background is more experimental condensed matter and I previously only thought of angular momentum with respect to electrons in a central potential where the selection rules are important. So can we learn anything from looking at the angular momentum of 'free' particles like electrons in a solid or excitations such as phonons and spin waves? –  Alexander Mar 11 '12 at 14:40