Photon mass

The subtracted radiatively corrected electron factor may be obtained from the subtracted one-loop electron factor in (9.10). To this end, one should restore the radiative photon mass in the one-loop electron factor, and then the polarization operator insertion in the photon line is taken into account with the help of the dispersion integral like one in (3.44) for the spin-independent... 

The uncertainty of this result arises from extrapolation to the zero photon mass limit. The magnitude of the nonlogarithmic coefficient in (9.44) seems to be quite reasonable qualitatively. Numerically the contribution to HFS in (9.44) is about 0.12 of the leading logarithmic contribution. 

From the hypothesis of a nonzero electrical conductivity in the vacuum and the corresponding dispersion relation [20,48, 50-52], the concepts of tired light and the observed cosmical redshift could be interpreted and associated with a nonzero photon mass of about 10 68 kg. The related frequency dependence can also become a measure of the mass. 

To calculate the photon masses, define the Higgs field by a small expansion around the vacuum expectations... 

If the mass of the photon is identically zero, its normalized helicity takes the values +1 and —1 because 7M is proportional to p1 [6]. The 0 component, which usually appears for a boson, is not considered but reappears if the photon has identically nonzero mass. In this case, the Wigner little group becomes 0(3). The 1 held corresponds to, for the photon with a tiny but nonzero mass because, as argued earlier, the structure of the 0(3) held equations is identical with that of the Lehnert equations [Eqs. (612)], which imply photon mass. Therefore p1 and, /M in the laboratory are infinitesimally different from light-like,... 

Therefore the fact that 9 is arbitrary in U(l) theory compels that theory to assert that photon mass is zero. This is an unphysical result based on the Lorentz group. When we come to consider the Poincare group, as in section XIII, we find that the Wigner little group for a particle with identically zero mass is E(2), and this is unphysical. Since 9 in the U(l) gauge transform is entirely arbitrary, it is also unphysical. On the U(l) level, the Euler-Lagrange equation (825) seems to contain four unknowns, the four components of , and the field tensor H v seems to contain six unknowns. This situation is simply the result of the term 7/MV in the initial Lagrangian (824) from which Eq. (826) is obtained. However, the fundamental field tensor is defined by the 4-curl ... 

The Lagrangian (824), which is the same as the Lagrangian (839), gives the inhomogeneous equation (826) using the same Euler-Lagrange equation (843). Therefore the photon mass can be identified with the vacuum charge-current density as follows (in SI units) ... 

This result, in turn, shows that the 0(3) equations in their condensed form, Eq. (612), indicate the existence of photon mass. This is precisely the result... 

Photon mass is shown to be self-consistent with 0(3) electrodynamics by considering the 0(3) Lagrangian [6] in reduced units ... 

The Lagrangian (850) shows that 0(3) electrodynamics is consistent with the Proca equation. The inhomogeneous field equation (32) of 0(3) electrodynamics is a form of the Proca equation where the photon mass is identified with a vacuum charge-current density. To see this, rewrite the Lagrangian (850) in vector form as follows ... 

In analogy with Eq. (845), the photon mass is defined in SI units by... 

Having derived the Proca equation in gauge-invariant form on the U(l) and 0(3) levels, canonical quantization can be attempted. Defining the photon mass in reduced units as... 

The first inference of photon mass was made by Einstein and de Broglie on the assumption that the photon is a particle, and behaves as a particle in, for example, the Compton and photoelectric effects. The wave-particle duality of de Broglie is essentially an extension of the photon, as the quantum of energy, to the photon, as a particle with quantized momentum. The Beth experiment in 1936 showed that the photon has angular momentum, whose quantum is h. Other fundamental quanta of the photon are inferred in Ref. 42. In 1930, Proca [43] extended the Maxwell-Heaviside theory using the de Broglie guidance theorem ... 

It can be seen that the photon mass is carried by, 4Vl 1 and Av(2 but not by 4Vl 1 . This result is also obtained by a different route using the Higgs mechanism in Ref. 42, and is also consistent with the fact that the mass associated with 4Vl 3 corresponds with the superheavy boson inferred by Crowell [42], reviewed in... 

If there is no vacuum polarization, then the photon mass resides entirely in the vacuum current. 

J. P. Vigier, New non-zero photon mass interpretation of the Sagnac effect as direct experimental justification of the Langevin paradox, Phys. Lett. A 234(2), 75-85 (1997). 

J. P. Vigier, Relativistic interpretation (with non-zero photon mass) of the small ether drift velocity detected by Michelson, Morley and Miller, Apeiron 4(2-3) (Special Issue The Field Beyond Maxwell) (April-July 1997). 

J. V. Narlikar, J. C. Pecker, and J. P. Vigier, Does a possible laboratory observation of a frequency anisotropy of light result from a non-zero photon mass Phys. Lett. A 154(5-6), 203-209 (1991). 

L. de Broglie and J. P. Vigier, Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection, Phy. Rev. Lett. 28(15), 1001-1004 (1972). 

L. de Broglie, and J. P. Vigier, Masse du photon, Effet Imbert et effet Goos-Hanchen en lumiere incidente polarisee (Photon mass, imbert effect and Gooshanchen effect in polarized light), C. R. Acad. Sci., Ser B (Sciences Physiques), 273B(25), 1069-1073 (1971). 

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