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trying to understand Photons & Gluons (both "actual" & "virtual")


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Q1: trying to denote spin, w/ subscripts, what prevents the "trifurcation" of photons:


[math]\gamma_{+\hbar} \longrightarrow \gamma_{+\hbar} + \gamma_{-\hbar} + \gamma_{+\hbar}[/math]


The above hypothetical photon decay could conserve all quantum numbers, as well as spin, and energy + momentum. So, what prevents (presumably?) such processes ?




Q2: If photons are spin=1... then why don't electrons, interacting w/ protons in atoms, constantly spin flip, each time they emit or absorb virtual photons ?

Q2': If virtual bosons can exist "off mass shell", w/ non-Einstein-equation-compliant combinations of momentum + energy... then can they also exist w/o the canonically required spin ?

Q2'': If actual photons carry oscillating EM fields... then do virtual photons, mediating and generating the scalar potential of particles, carry scalar potential ? Are they "scalar potential" photons, representing quantized amounts of scalar potential (as opposed to actual photons, which carry quantized amounts of vector potential, whose plane of oscillation is their plane of polarization, etc.) ?




Q3: If gluons are spin = 1... then how could gluons "bifurcate" (as depicted in some Feynman Diagrams),


[math]g_{+\hbar} \longrightarrow g_{+\hbar} + g_{\pm\hbar}[/math]


w/o violating spin conservation ?

Q3': Or, do virtual gluons not need to conserve spin ?

Q3'': In 3-jet decays, in particle colliders, one of the jets derives from a spin-1 gluon... is that gluon an "actual" and "promoted" gluon (to quote Gary Zukov's Dancing Wu Li Masters), as opposed to "virtual" gluons mediating the strong / color force w/in nucleons ?

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Q1: I too believe it's not a matter of conservation of quantum numbers. Photons just don't interact among themselves in vacuum. Something like: vacuum behaves linearly for E and H.


Though, in nonlinear matter, they do. Two or three photons combine to make one in optical frequency doublers and triplers. Or they can add or subtract their frequency, just like a heterodyne. Don't add and subtract quantum numbers there, because of the many electrons involved.


Not very easy, because light uses to make an electric field much smaller than atom nuclei do. It needs special crystals (asymmetric ones for frequency doublers, that's uncommon) AND very intense light, which means concentrated spatially from a pulsed laser, typically Yag. If the doubler is within the cavity of the laser, better: stronger field, and the filters that pass the harmonics can feed the rejected fundamental back in the amplifier. The crystal must also be long enough to act, but the phases of the fundamental and harmonic must match over this length, which is difficult.


First fun: people make nice nonlinear (quadratic, for a tripler cubic) equations to show the cos(w1*t)*cos(w2*t) term which gives cos[(w1-w2)*t] and cos[(w1+w2)*t]... and carefully forget the existence of photons for that hattrick. Shush!


Second fun: if the field intensity suffices, light can ionize atoms despite the photon energy is too low. It happens with concentrated pulsed lasers and air's nitrogen. Called "multi-photon ionization". I like to imagine it that way: if light's field is smaller than the nucleus' one, light must use the atom's resonance and take time to eject an electron, while strong light does not need the resonance.


Third fun: the energy of cosmic rays is allegedly limited by some mechanism where a too strong cosmic ray gives energy to a photon from the 3K background. Forgotten the details - some particle pair in between? This would indeed be an indirect photon-photon interaction, though not at technological energies.


The very existence of cosmic rays must put a limit to any nonlinearity of vacuum regarding the electromagnetic field - a limit possibly much stronger than human experiments do.

Q2 bis: electrons' spin interacts faintly with the EM field. It makes no electric field by itself, only a magnetic dipole, whose interaction with the nucleus' magnetic dipole is faint, making the hyperfine structure. For an isolated hydrogen atom, the interaction takes typically 10 million years


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intuitively, for one electron, to simultaneously absorb two (or more) photons, would require the simultaneous overlap, of all of the involved wave-functions (in a quantum equivalent, of a multi-body collision). If so, then that would inform you of the necessary photon density (assuming photon wave-functions are of order their wavelengths across).


If so, then the multiple simultaneous overlap of several wave-functions seems somewhat similar, to the "Rydberg blockade" effect, crucial to the formation of "photonic molecules", when (seemingly) several atomic wave-functions are overlapping, so that excitation of one excludes excitation of overlapping nearby wave-functions (??)




a quick Google'ing for particle decay rates and "mass squared" seemingly suggests that decay rates are proportional to mass squared (not inversely so) -- do not more massive particles decay more quickly, e.g. top quark as an extreme example (??)

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