Self-consistent effects 0 electrodynamics

The inverse Faraday effect depends on the third Stokes parameter empirically in the received view [36], and is the archetypical magneto-optical effect in conventional Maxwell-Heaviside theory. This type of phenomenology directly contradicts U(l) gauge theory in the same way as argued already for the third Stokes parameter. In 0(3) electrodynamics, the paradox is circumvented by using the field equations (31) and (32). A self-consistent description [11-20] of the inverse Faraday effect is achieved by expanding Eq. (32) ... 

In the presence of matter (electrons and protons), the inhomogeneous field equation (32) can be expanded as given in Eqs. (52)-(54) and interprets the inverse Faraday effect self-consistently as argued already. Constitutive relations such as Eq. (55) must be used as in U(l) electrodynamics. 

The 0(3) Proca equation (856) does not have this artificial constraint on the potentials, which are regarded as physical in this chapter. This overall conclusion is self-consistent with the inference by Barrett [104] that the Aharonov-Bohm effect is self-consistent only in 0(3) electrodynamics, where the potentials are, accordingly, physical. 

These field equations are therefore the result of a non-Abelian Stokes theorem that can also be used to compute the electromagnetic phase in 0(3) electrodynamics. It turns out that all interferometric and physical optical effects are described self-consistently on the 0(3) level, but not on the U(l) level, a result of major importance. This result means that the 0(3) (or SO(3) = SU(2)/Z2) field equations must be accepted as the fundamental equations of electrodynamics. 

Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

Thus, at the modern level of the relativistic electronic structure theory, the problem of defining ground states of elements heavier than 122 remains. Very accurate correlated calculations of the ground states with inclusion of the quantum electrodynamic (QED) effects at the self-consistent field (SCF) level are needed in order to reliably predict the future shape of the Periodic Table. At the time of writing, an accepted version of the Table is that of Fig. 1, with the superactinides comprising elements Z = 122 through 155 as suggested in [1, 2]. 

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