Transverse photons

One then proves in the manner employed in the one-particle case that if. .. Wn 0 and Wl... is a transversal photon amplitude, i.e.,... 

To order e2 the Coulomb interaction term contributes to the first-order term in the 5-matrix expansion, i.e., to fd4xJffin(x), and the term contributes to second-order. Diagrammatically, we have illustrated these contributions in Fig. 11-1 ( stands for Coulomb, / for transverse photons). To the order indicated, the part of the 5-matrix contributing to the process is... 

With a nonzero rest mass one would at a first glance expect a photon gas to have three degrees of freedom two transverse and one longitudinal. This would alter Planck s radiation law by a factor of, in contradiction with experience [20]. A detailed analysis based on the Proca equation shows, however, that the B3 spin field cannot be involved in a process of light absorbtion [5]. This is also made plausible by the present model of Sections VII and VIII, where the spin field is carried away by the pilot field. As a result, Planck s law is recovered in all practical cases [20]. In this connection it has also to be observed that transverse photons cannot penetrate the walls of a cavity, whereas this is the case for longitudinal photons which would then not contribute to the thermal equilibrium [43]. 

The x and polarizations (or any combination) are the familiar transverse photon and the transverse wave. The z polarization along the line of propagation gives the longitudinal photon and the longitudinal EM wave. 

But now, if there is a ample evidence of nonzero photon mass, the question of absorption or emission amplitudes for longitudinal photon has to be answered in a consistent manner. Goldhaber and Nieto [49] showed that these are suppressed in comparison with their transverse counterparts by a factor The corresponding rates and cross sections are suppressed by the square of this factor. The quantum mechanical matrix element for ordinary transverse photon is given by Tf(x,y) = (f JX)y i) for a photon-induced transition to an arbitrary state/, where i is the initial target state. The corresponding matrix for a longitudinal photon is... 

The relativistic correction to the fermion kinetic energy is represented as a potential. The Breit-Fermi interaction includes the effects of transverse photon exchange as well as relativistic corrections to Coulomb photon exchange. The potentials are given with the assumption that the states acted on are S states with total spin 1. 

Fig. 1. Two-electron Feynman diagrams representing electron interaction in the second order. Solid line corresponds to electrons, dotted line corresponds to the Coulomb photons, wavy line corresponds to transverse photons (Breit interaction). If A = A and B1 = B then the diagram is called direct , otherwise, if A = B and B = A the diagram is called exchange . Letters A, B denote one-electron state...

The transverse photon line attached to this vertex (at the point x) is u>... 

An additional line ( two-transverse-photon-recoil line) appears to be ------------- ... 

The one-transverse-photon nuclear recoil correction corresponds to the diagrams shown in Fig. 2. One easily obtains... 

The two-transverse-photon nuclear recoil correction is defined by the diagram shown in Fig. 3. We find... 

Fig. 5. Two-electron one-transverse-photon nuclear recoil diagrams...

Fig. 6. Two-electron two-transverse-photon nuclear recoil diagram...

An additional line ( two-transverse-photon-recoil line) appears to be... 

An alternative coupling scheme, that proves to be advantageous in many regards, and is now the preferred theoretical method, is the multipolar framework [32, 33] of molecular QED. In this formulation, molecules couple directly to the radiation fields through their molecular multipole moments. Because the Maxwell fields obey Einstein causality, interactions between species is properly retarded, which is mediated by the emission and absorption of transverse photons. It is convenient to partition the total many-body QED matter-field multipolar Hamiltonian into a sum of parficle, radiation field, and interaction terms as follows ... 

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