Virtual photon coupling

This term is then a sum over all possible fluctuations of the that couple to the virtual photon coupled to the electrons. This means that the propagator is of the form... 

By introducing the formalism of virtual photon coupling, the timescale for cooperative absorption, t, can be interpreted in terms of a range of propagation for which the exchanged photon has virtual character. Thus the distance R between two molecules that cooperate in the absorption process must be subject to the condition... 

If the photon energy hcoi is anywhere near to the excitation energy E o, it is clear from Eqs. (2.7) and (2.8) that where virtual photon coupling is involved, the distributive mechanism will only be effective over a much shorter range than the cooperative mechanism. For example, if E o/h = 5 x 10 Hz, we have 0.15 /im. 

In this mechanism, two-photon transitions are forbidden and the excitation of the participating molecules occurs through one- and three-photon allowed transitions. Both the real (laser) photons are absorbed by one molecule, excitation of its partner resulting from the virtual photon coupling. Because of the difference in selection rules from the previous case, the first two terms of Eq. (5.13) are now zero, and contributions arise only from the third and fourth terms. It must also be noted that setting the two absorbed photon frequencies to be equal in Eq. (5.16) to produce zJy, (co,o>) introduces index symmetry into the tensor, as indicated by the brackets embracing the first two indices. A factor of j must then be introduced into the definition of this tensor in order to avoid over-counting contributions. The transition matrix... 

In the distributive mechanism two photons with frequencies (coq + and (coq — undergo concerted absorption at the same center, and the energy mismatch Ej.. is conveyed to another molecule by virtual photon coupling, as in Fig. 3. In this case, using exactly similar methods, the following rate equation is obtained ... 

Even if there is no electromagnetic field present, the vector potential exhibits fluctuations A = (4 ) + 84, so that even if there is only the vacuum, physics still involves this fluctuation. This is also seen in the zero-point energy of the harmonic oscillator expansion of the fields. So an electron will interact with virtual photons. If we represent all of these interactions as a blob coupled to the path of an electron, this blob may be expanded into a sum of diagrams where the electron interacts with photons. Each term is an order expansion and contributes... 

Bound-state QED provides a proper and practicable description of few-electron systems. Both QED-radiative corrections and electron-electron interactions may be treated perturbatively with respect to the coupling a — e2, counting the number of virtual photons involved, while the interaction with the external nuclear fields is included to all orders in Za. 

The main application of bound-state QED is the evaluation of energy levels of few-electron atoms. The energy levels appear as a series of even powers of the coupling with the radiation field since only virtual photons, each of which enters with two powers of the coupling constant (e2), are involved... 

As seen above, synergistic two-photon absorption can in principle take place by either or both of the mechanisms, where (i) each laser photon is absorbed by a different molecule (the cooperative mechanism), or (ii) both laser photons are absorbed by a single molecule (the distributi e mechanism). In each case, the energy mismatch for the molecular transitior s is transferred between the molecules by means of a virtual photon that couples with each molecule by the same electric-dipole coupling as the laser photons. The result, however, is a significant difference in the selection rules applying to the two types of processes. 

From Eqs. (5.4) and (5.5) it follows that each appearance of is associated with the creation or annihilation of a photon. It is thus readily apparent that the first non-zero contribution from Eq. (5.7) is the fourth-order term, corresponding to four separate photon creation and annihilation events these comprise the two annihilations of real photons from the incident light, and the creation and annihilation of the virtual photon which couples the two molecules. 

Atoms (ions) encapsulated into small-diameter (-1 nm) metallic carbon nanotubes may form quasi-one-dimensional atomic polariton states via strong coupling to the virtual photonic modes of the nanotube. This results in sizable amounts of the two-qubit atomic entanglement that persists with no damping for very long times. We expect this effect to stimulate relevant experimental efforts and thus to open a path to new device applications of atomically doped carbon nanotubes in quantum information technologies. 

The reason for the latter lies in the narrowness of these particles one can simply miss them as one varies the energy. On the other hand, once discovered, the fact that J/ (3097), T(9.46) and the Z are vector particles 1, and thus couple naturally to a virtual photon, makes an e+e ... 

Since the J/ i family is directly and copiously produced in the e" e annihilation channel, the simplest conjecture is that it has the quantum nmnbers of the photon. e" "e cannot decay into one real photon because of momentum conservation but it can couple to one virtual photon, or to two (or more) real or virtual photons. 

The dominant lowest order coupling is to one virtual photon, so the simplest assumption is that J/ J is a = 1 state reached through one virtual photon exchange via mechanisms familiar from the theory of vector meson dominance used in discussing the u , 0 mesons. Fig. 11.9 shows various possibilities for the process e+e —> / in the region of the J/ mass. 

With a traveling fellowship awarded by Harvard, Slater spent his first postdoctoral year at Cambridge. There, he developed a theory on radiative transitions in atoms. On discussing this idea with Neils Bohr and Hans Kramers, a joint paper on the quantum theory of radiation was published in 1924. However, Bohr and Kramers altered Slater s original idea by ascribing a virtual existence to the photons in the transitions— not the real photons that Slater believed in. In early 1925, Slater was back at Harvard and published further work of his own on radiative transitions. He presented a picture of absorption and emission of real photons coupled with energy conservation in transition processes. He also established a relationship between the width of spectral lines and the lifetimes of states. 

The total Lagrangian X = JS G + JS D + JS , then involves the interaction between fermions and the gauge field. The Dirac field will be generically considered to be the electron and the gauge theory will be considered to be the non-Abelian electromagnetic field. The theory then describes the interaction between electrons and photons. A gauge theory involves the conveyance of momentum form one particle (electron) to another by the virtual creation and destruction of a vector boson (photon) that couples to the two electrons. The process can be diagrammatically represented as... 

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