# Spin of quasiparticle formed by photon in glass

This previous question about the effective mass of a photon traveling through glass has a few answers that say we can think of it as a quasiparticle with an effective mass. Photons are spin-1, but because they move at the speed of light, we only get two polarizations. In glass, is the resulting quasiparticle also spin-1? If so, how would one measure the spin?

I think that you should take @tparker's comment on the top-rated answer there to heart: a photon (or photon-like quasiparticle) in glass is not massive, and in particular you should be very careful to distinguish this situation from that of a photon in a superconductor, which really does acquire mass due to the Higgs mechanism.

There are various ways to arrive at this conclusion, but I still favor the approach I used in a related discussion. Mass is, by definition, intrinsic energy- the minimal energy required to create an object and the energy that remains in it when all other energy (such as kinetic) has been removed. What is the minimum energy required for a photon in glass? There is none. You can always make a longer wavelength excitation and get to arbitrarily low energy. In the parlance of condensed matter physics, we say that this quasiparticle is "gapless."

If you suppose that this is not true- maybe the mass is just so low that we don't normally notice it- you get predictions that a low energy photon coming from the vacuum, with less mass than the quasiparticle, couldn't enter the glass and would always be reflected. This violates Maxwell's laws and their generalizations to media, which say that in a linear medium like idealized glass the reflection is not amplitude dependent. You can make similar arguments about spin: if you created an $$S_z=0$$ photon in the medium, and it reached the boundary, what would happen to it?

In the "real" world of fundamental physics, everything transforms nicely under a Lorentz transformation and anything that has a speed less than $$c$$ is massive. However, any notion of a photon quasiparticle in a material lives in the low-energy effective field theory world, where neither of these is necessarily true. This is what makes condensed matter physics so rich and interesting- inside of materials, you can effectively realize entirely new worlds with different emergent laws of nature.

Summarizing: a photon quasiparticle in an ideal linear medium travels below $$c$$ but still retains its photon-ness in many respects: it is massless and spin-1 with two possible polarizations.

Edit: For completeness, the argument that tparker suggests is related to the Ward identity- see this question (for example). The presence of a linear medium renormalizes the permittivity and permeability, but this process otherwise does not change the photon propagator.

• The "massive" nature I'm looking for would come from a dispersion relation of the form E² = α + βp² where α, β > 0, so α is analogous to mc². Is the dispersion relation in glass not of that form? This answer about photons behaving massively in a superconductor says, "Photons in a waveguide or a plasma have cut-off frequencies $f_C$ and follow the equations of particles with rest mass $m_0 = hf_C/c^2.$" Would an optical fiber allow a spin/polarization measurement with three outcomes? – Mike Stay Nov 19 '20 at 19:39
• "Is the dispersion relation in glass not of that form?" It is not. You can see this at the level of Maxwell's equations; the values of the permittivity and permeability are modified but the functional form of the all the equations remains the same, and in particular you still have E=vp. – Rococo Nov 20 '20 at 0:19
• In a nonlinear medium, such as waveguides / plasma / superconductors, many things are possible. But in general, a gapped dispersion relation will not imply a third polarization mode. That degree of freedom has to come from somewhere. In the Higgs mechanism, roughly speaking, a degree of freedom goes from being associated with the matter field (and its gauge) to being associated with the EM field (as discussed in Ron's answer to the question you link to). In, say, a waveguide, nothing of this sort happens. The modes are modified from vacuum, but you can't get any new ones. – Rococo Nov 20 '20 at 0:19
• Oh, I should clarify though. In a waveguide, there are indeed no new modes, but the modes can be part transverse and part longitudinal. So it is an interesting intermediate case, in that sense, between vacuum (two polarization modes, both transverse) and a superconductor (three polarization modes, two transverse and one longitudinal). – Rococo Nov 20 '20 at 1:05