photon matrix - SMARTPHONE
A single photon can be in a mixed state. (5) For unpolarized light in particular, the idea that the density matrix implies that each photon has a definite polarization is incoherent. For example, in the {x,y} eigenbasis (= {x-polarization, y-polarization}), one way to represent unpolarized photons is with the density matrix One participant questions the appropriate matrix element for jj coupling, suggesting it differs from the electric dipole matrix element used in LS coupling.
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Another participant emphasizes that selection rules are based on angular momentum conservation and discusses the implications of photon polarization on these rules. Your H +/- matrix, and posts on this thread seem to be taylor made for it. My "photon matrix" (I'm not sure that it is a true matrix) is 13 x 70, and includes all resonant vibrational potentials between frequency and wavelengths of light. Thus you can change the polarization matrix according to (3) which corresponds to the radiation gauge of the free photon field to with an arbitrary vector field .
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When you sum over photon polarization vectors, some gauge vector, r, enters the calculation (see page 4). By making the following clever choice for the gauge vector: r = (0,1,i,0), a lot of terms drop out during the calculation. Of course, once you have made this explicit choice for the gauge vector you will have to stick it! The discussion revolves around the interpretation of the spin of photons, specifically the claim that they have spin zero. Participants explore the implications of this claim and its mathematical underpinnings, as well as contrasting views on the actual spin of photons.
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One participant questions the interpretation of photons having spin zero and suggests that it may relate to the proper time ... So what you're saying is that in the case of an electromagnetic field, even though it's a Tensor field (just like gravity), and the carrier of the electromagnetic field is a spin-1 vector particle, the photon, the tensor can be broken down into sub-vectors? Electromagnetic field 4-potential is a 4-dimensional vector. So, the incident photon interacts with the free (weakly bounded) electron in the Compton scattering and transfers partially momentum and energy to that particle, but it remains the same photon, carrying the typical Planck amount of action (energy*time).