polarized photons

[Norman Albers]

Can there be a single plane-polarized photon? One one hand they are bosons and I read that massless bosons are disallowed the zero spin state. (For masses, rules say <+L,-L> including integer states between.) Don't they have to carry angular momentum? How then can there be plane polarization, which we can see as superposition of opposite helicities, without two photons' worth of energy present?

[timo]

Can there be a single plane-polarized photon?

Sure.

One one hand they are bosons and I read that massless bosons are disallowed the zero spin state.

Not true in general but true for vector-bosons (so it is true for photons).

 

How then can there be plane polarization, which we can see as superposition of opposite helicities, without two photons' worth of energy present?

If the spin-base for your state is {|u>, |d>} where the two base vectors are left-handed and right-handed polarisation, then you can construct a linear polarisation by |state> = (|u> + |d>)/sqrt(2), for example. It´s a pure one-photon state - it´s only not an eigenvector to the helicity operator.

[Norman Albers]

Whoa, Betty! Don't they always carry angular momentum coming out of interactions with particles? Then again, going into detectors?

[swansont]

What you'll find if you look at specific transitions is thet an m=0 state will not couple to another m=0 state if the overall angular momentum hasn't changed. So a polarized photon in that case has to be viewed as a superposition of the two opposite circular polarizations.

[Norman Albers]

I am productively confused. Can a plane-(PP) wave be absorbed spectrally?.........I thought <L> had to change by one unit.

[Perturbation]

Also, the transverse polarisations of a photon cannot emerge in practice due to the Ward identity of QED.

 

[math]k_{\mu}\cal{M}^{\mu}[/math][math]=0[/math]

 

Where M is the matrix element arising from a scattering process involving a photon with four-momentum k.

[swansont]

I am productively confused. Can a plane-(PP) wave be absorbed spectrally?.........I thought <L> had to change by one unit.

 

Sorry, I misrepresented something earlier. I should have used states with the same F (total angular momentum) not two states with the same L. So you can keep the total angular momentum the same but not for m=0 -> m=0.

 

e.g. in tables 10 and 13 of this paper (pfd file) you can see that the Clebsch-Gordan coefficient for the transitions involving no change in F and m=0, is zero.

[Norman Albers]

I'll look around because I'm not sure what your notation of "F" is but are we talking about like J(J+1), or its SQRT?

[Perturbation]

I'll look around because I'm not sure what your notation of "F" is but are we talking about like J(J+1), or its SQRT?

 

[imath]j(j+1)\hbar^2[/imath] are the eigenvalues of the norm of the angular momentum operator [imath]J^2=J^2_x+J^2_y+J^2_z[/imath]. The squareroot is for the J.

[swansont]

I'll look around because I'm not sure what your notation of "F" is but are we talking about like J(J+1), or its SQRT?

 

 

F is the sum of all the angular momenta of the atoms, J is the total momentum of the electron alone. J = S + L, F = J + I (S is electron spin, L is orbital, I is nuclear spin)

[Perturbation]

Also' date=' the transverse polarisations of a photon cannot emerge in practice due to the Ward identity of QED.

 

[math']k_{\mu}\cal{M}^{\mu}[/math][math]=0[/math]

 

Where M is the matrix element arising from a scattering process involving a photon with four-momentum k.

 

And that should say longitudinal.

[Norman Albers]

Thanks, Perturbation, my QED book goes to that point of developing the four modes and saying scalar and longitudinal cancel, or something like that: this is the limit of my exposure but I can speak your language almost. I just went ahead and put a charge sheath (long-scalar mode) into my semiclassical description. Take me further into current theory. I have assumed that the not-vacuum can supply 'infinitesimal' charge in dipolar 'plasma' form in photon fields. I understand that we speak of scalar photon exchange manifesting the Coulomb force.

[Perturbation]

Huh? Are you saying that the Coloumb potential is a result of the exchange of a scalar photon? In a Coloumb field we still have exchanges of vector bosons, the magnetic potential is simply zero. This isn't the same thing as exchanging a scalar.

 

The "non-vacuum" supplying a charge sounds like vacuum polarisation, but I don't think this is what you're trying to say.

[Norman Albers]

I am probably being messy about the first part of your response and shall go back over that part of the book which is about as far as I have gotten in my isolation. As to the second part, yes! Can you help me in 200 words or less? I am not near a major school, have done some interesting work in semiclassical fields, and need to choose how and what to learn further, given that books aren't cheap and my time is not free. I serious appreciate being told what I should learn, and I ask you to look at what I see from my perspective. Norm Albers

[Perturbation]

Actually I just wrote a simplish explanation of virtual particles for someone. It's the post with the Feynman diagrams in it

 

Virtual Particles

[Norman Albers]

Thanks, I will hang out with that. I read in Cohen-Tannoudji's "Photons and Atoms", on p.378, they have expressed normal variables of the field in Lorentz gauge. "energy associated with the longitudinal variables compensates exactly that associated with the scalar variables, the only contribution being provided by transverse variables." This is about as far as I have gone.

[Norman Albers]

I inhabit the realm of differential vector calculus. Only now can I see why I worked by defining "A" in y-hat(cosX) + z-hat(sinX). There is subtle confusion if you try to represent <y,z>-hats as the real and imaginary components of e^ikX. The "A" above is what maps to plus or minus one times itself, if you consider also the opposite sign on the z-component. Constructing an eigenvector for zero demands supersposition, though. Witness: We might try to say, A=y-hat (e^ikX) looks like a plane wave and works if we take only real components. If you try to say, A is only y-hat(cosX), then curls puts this into z-hat, essentially a complex eigenvalue because you have rotated the phase. Is this why we invented vector bosons? If we want to use complex notation do we build plane waves as A+A* (normalized) and this all works because A* is the opposite spin? Am I getting somewhere? To construct my original "A", I would have to write: y-hat(A+A*) - z-hat(i)(A-A*). This can be rewritten: A(y-hat + iz-hat) + cc. This seems to be the only way to make complex notation work in the real domain! If you Fourier transform everything, complex quantities are no longer an embarasssment. We all agree, though, that "fields we experience" must come out real. I feel not quite finished here.

[Severian]

Incidentally, if you had a scalar with the same quantum numbers as the photon (and a coupling to the photon obviously) it would mix with the photon to give the photon a mass. This is exactly what happens to the Z-boson. The Higgs scalar field provides the longitudinal component of the Z boson's spin.

[Norman Albers]

Help, I'm being Shanghai'd by QFT!!! Thank you mate, and sorry for my edit confusion which is now at rest. Nothing is necessarily obvious to me, though I am primed to catch up to what you are offering. We are getting warm, as per my "excuses" mention of Higgs. We are all somehow talking about the same stuff; there is nowhere to hide, but I think we are not finished. I don't expect to add much about your fine structures at their level. However, Ledermann admitted we are clueless about the twenty or so constants which flesh out the Standard Model. I think it is time we finished all this business.

[Norman Albers]

I shall refresh the ENTIRE topic of vector model of atoms, which was slightly more rusty than I knew, but this won't take long. Nice table for Clebsch-Gordon coeffs., with a zero symmetrically in the center <m=0> . What to you is the helicity op.? To me it is curl. I appreciate QM for vocabulary that's minimal and accurate. My papers do accounting of inhomogeneous fields and my goal is to interpret what is necessarily so insofar as such equations are still to be considered useful. You say "quanta" and that is a nice word for what I call a "bound state". Can you relate to that word? My whole understanding is that we stop thinking mass is anything but energy localized for a spell. LIGHT IN A BOX, a very serious concept given my A_phi solution. . . . . . . In photons, can you relate to my angular momentum density of: A-cross-[A-dot + del(U) - (rho)r] ? How do you describe the ang. mom. of the (pi)-polarized (am I getting hip?) case? PERTURBATION: Now we are getting hot. I say electrons can be considered as nothing but a construct of polarization. The polarization crunch which needs to yield a positive "4pi" at an inner limit can be thought to cancel what we thought was a negative delta function we needed in introduce. They cancel, or maybe don't exist??? I think of one over r-squared as a mode of the field available upon this dipole stuff poking in (arbitrary to out) at arbitrarily high intensities.

if you had a scalar with the same quantum numbers as the photon (and a coupling to the photon obviously) it would mix with the photon to give the photon a mass

. SEVERIAN, I got nervous but I do see exactly how you use these words now. No problem getting started, anyway.

[Norman Albers]

if you had a scalar with the same quantum numbers as the photon...

Scalar what? I have only partly done the Fourier transform of my photon field and don't know what to say about it yet. I have allowed what I think is a scalar-longitudinal manifestation without mass. Divergence of "A" gives "U" which gives rho but I simply allow the fields to cook these things up. I assume there may be regions of diverging E-field; this is simply what you declare by saying "quasi-monochromatic wave packet". Energy sloshes back and forth, positive and negative, in the "accordian" mode. This seems like internal business related to the structure rather than propagating energy. I have longitudinal terms under FT so I use that word, and I have a scalar potential, so I use also that word. Can you folks help me by saying more of where these two manifest in QED? It is exciting to be almost talking the same language and I think if we both (all) make the effort we might really get somewhere. I am just coming out of confusion to say that there are not separate homogeneous and inhomogeneous field "backgrounds". I got confused by the good question, "what is epsilon-nought?" To me it is just a coupling constant and my physics is describing that phased-array antenna which manifests the entire field.

[Norman Albers]

If the circularly polarized photon is passed through a plane-polarizing filter, do we get half a chance of a plane wave being transmitted? If so, was there angular momentum given to the filter?

[Meir Achuz]

If the circularly polarized photon is passed through a plane-polarizing filter, do we get half a chance of a plane wave being transmitted? If so, was there angular momentum given to the filter?

I just noticed this question.

The answers are Yes and Yes.

[Severian]

Scalar what?

 

A scalar particle, i.e. with no spin.

[Norman Albers]

Thank you both. Meir, isn't this angular momentum transfer to the filter a sometimes unaccounted piece of the puzzle? I don't yet see specifically where but I think this is a worthy question. Polarizers are part of non-locality detections, yah?