Electron-positron virtual pairing electrodynamics, quantum

The anomalous contribution to the magnetic moment of an electron has been explained by the quantum electrodynamic theory. The additional contribution—the radiative correction —arises from the interaction of the electron-positron virtual pair emitted and absorbed by the real electron. A theoretical expression in terms of the fine structure constant a is... 

A further term, which has no analogue in hydrogen, arises in the fine structure of positronium. This comes from the possibility of virtual annihilation and re-creation of the electron-positron pair. A virtual process is one in which energy is not conserved. Real annihilation limits the lifetimes of the bound states and broadens the energy levels (section 12.6). Virtual annihilation and re-creation shift the levels. It is essentially a quantum-electrodynamic interaction. The energy operator for the double process of annihilation and re-creation is different from zero only if the particles coincide, and have their spins parallel. There exists, therefore, in the triplet states, a term proportional to y 2(0). It is important only in 3S1 states, and is of the same order of magnitude as the Fermi spin-spin interaction. Humbach [65] has given an interpretation of this annihi-... 

Although the proper point of departure for relativistic atomic structure calculations is quantum electrodynamics (QED), very few atomic structure calculations have been carried out entirely within the QED framework. Indeed, almost all relativistic calculations of the structure of many-electron atoms are based on some variant of the Hamiltonian introduced a half century ago by Brown and Ravenhall [1] to understand the helium fine structure. By decoupling the electron and radiation fields in QED to order a (the fine-structure constant) using a contact transformation. Brown and Ravenhall obtained a relativistic momentum-space Hamiltonian in which the electron-electron Coulomb interaction was surrounded by positive-energy projection operators. Owing to the fact that contributions from virtual electron-positron pairs are automatically projected out of... 

Moreover, electron-positron pair creation and other proce.s.ses ( radiative corrections ) de.scribed by quantum electrodynamics which has quantized degrees of freedom for both the fermions and the electromagnetic field are usually not included in the theory, although the chaige-conjugated degrees of freedom are still there. Therefore the literature often refers to the no virtual pair or, in short, no pair approximatioa Very few calculations go beyond this approximation. " Nevertheless. the no-pair operator based on the DCB Hamiltonian provides an exellent approximation to the full theory, generally sufficient for the determination of relativistic effects in the electronic structure of neutral atoms and molecules. 

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