The derivation of a convergent series representation for the quantum electrodynamic effective action obtained by two of us (is reexamined. We present more details of our original derivation. Moreover, we discuss the relation of the electric-magnetic duality to the integral representation for the effective action, and we consider the application of nonlinear convergence acceleration techniques w...

An r-commutative algebra is an algebra A equipped with a Yang-Baxter operator R:A ⊗ A → A ⊗ A satisfying m = mR, where m:A ⊗ A → A is the multiplication map, together with the compatibility conditions R(a⊗ 1) = 1 ⊗ a, R(1 ⊗ a) = a ⊗ 1, R(id ⊗m) = (m ⊗ id)R2R1 and R(m ⊗ id) = (id ⊗ m)R1R2. The basic notions of differential geometry extend from commutative (or supercommutative) algebras to r-comm...

It was known that the quaternion group and the octic group could not be generated by the squares of any group [5, pp. 193-194]. A natural question is which groups are generated by the squares of some groups. Clearly, groups of odd order and simple groups are generated by their own squares. In this paper, we show in a concrete manner that abelian groups are generated by the squares of some group...

The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in αZ is formulated. The nuclear recoil corrections for atoms with one and two electrons over closed shells are considered in detail. The problem of the composite nuclear structure in the theory of the nuclear recoil effect is discussed.

Accurate calculations of the binding energies, the hyperfine splitting , the bound-electron g-factor, and the parity nonconservation effects in heavy few-electron ions are considered. The calculations include the relativistic, quantum electrodynamic (QED), electron-correlation, and nuclear effects. The theoretical results are compared with available experimental data. A special attention is foc...

Using the Lagrangian that was developed on the corresponding principle between the moving medium electrodynamic and quantum field theory the explicit expression for the static polarizability vertex has been obtained. The applications of this vertex for calculations of real Compton scattering amplitude as well as the imaginary part of doubly virtual Compton scattering amplitude have been demonst...

Received 16 June 2021DOI:https://doi.org/10.1103/PhysRevA.103.069902©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMolecular spectraRelativistic & quantum electrodynamic effects in atoms, molecules,& ionsAtomic, Molecular Optical

One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on that space preserving the non-commutative structure constitute a quantum group. The noncommutativity of these variables provide an example of non-commutativ...

Cavity quantum electrodynamic (QED) effects are studied in semiconductor microcavities embedded with InGaAs quantum dots. Evidence of weak coupling in the form of lifetime enhancement (the Purcell effect) and inhibition is found in both oxide-apertured micropillars and photonic crystals. In addition, high-efficiency, low-threshold lasing is observed in the photonic crystal cavities where only 2...

In this paper, imposing hermitian conjugate relations on the two– parameter deformed quantum group GLp,q (2) is studied. This results in a non-commutative phase associated with the unitarization of the quantum group. After the achievement of the quantum group Up,q (2) with pq real via a non–commutative phase, the representation of the algebra is built by means of the action of the operators con...