Quantum self energy

Expression (9.15) gives the total electrostatic energy and not the cohesive energy of a molecular crystal. It ignores the quantum-mechanical nature of the charge distribution an electron cannot interact with itself, but just such a self-energy is included in the expression. 

When innermost core shells must be treated explicitly, the four-component versions of the GREGP operator can be used, in principle, together with the all-electron relativistic Hamiltonians. The GRECP can describe here some quantum electrodynamics effects (self-energy, vacuum polarization etc.) thus avoiding their direct treatment. One more remark is that the... 

It is not possible for conventional electromagnetic models of the electron to explain the observed property of a point charge with an excessively small radial dimension [20]. Nor does the divergence in self-energy of a point charge vanish in quantum field theory where the process of renormalization has been applied to solve the problem. 

Heitler spoke on the quantum theory of damping, which is a heuristic attempt to eliminate the infinities of quantum field theory in a relativistic invariant manner, Peierls spoke of the problem of self-energy, and Op-penheimer gave an account of the developments of the last years in electrodynamics in which he discussed the problem of the vacuum polarization and charge renormalization with special reference to the recent work of Schwinger and Tomonaga. 

The vacuum polarization is well known to have an analog in quantum electrodynamics [46], the photon self-energy. The latter has no classical analog on the U(l) level, but one exists on the 0(3) level, thus saving the correspondence principle. The classical vacuum polarization on the 0(3) level is transverse and vanishes when oo = 0. It is pure transverse because, as follows, the hypothetical E0) field is zero on the 0(3) level... 

The physical sense of this expressions is quite transparent, they describe the quantum amplitudes of the scattering processes. Three functions scattering state in the Landauer-Biittiker theory. Note, that G here is the full GF of the nanosystem including the lead self-energies. 

Such comparisons promise interesting tests of QED. Unfortunately, however, the theory of hydrogen is no longer simple, once we try to predict its energy levels with adequate precision [36]. The quantum electrodynamic corrections to the Dirac energy of the IS state, for instance, have an uncertainty of about 35 kHz, caused by numerical approximations in the calculation of the one-photon self-energy of a bound electron, and 50 kHz due to uncalculated higher order QED corrections. 

Abstract. Measurements of the 25i/2 2Pi/2 and 2Si/2 2P3/2 transitions in moderate Z hydrogen-like ions can test Quantum-Electrodynamic calculations relevant to the interpretation of high-precision spectroscopy of atomic hydrogen. There is now particular interest in testing calculations of the two-loop self-energy. Experimental conditions are favorable for a measurement of the 25i/2 2P3/2 transition in using a carbon dioxide laser. As a preliminary experiment, we have observed the 2S1/2 2P3/2 transition in using a 2.5 MeV/amu foil-stripped ion beam and a continuous-wave... 

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