Modern Physics Letters A

Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum electrodynamics provides us with accurate theoretical predictions for the transition energies relevant to simple atomic systems, and steady theoretical progress relies on advances in calculational techniques, as well as numerical algorithms. In this brief review, we discuss one particular aspect connected with the recent progress: the evaluation of relativistic corrections to the one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge number, for excited non-S states, up to the order of α(Zα)⁶ in units of the electron mass. A few details of calculations formerly reported in the literature are discussed, and results for 6F, 7F, 6G and 7G states are given.

On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is closely connected to the familiar Laplace–Runge–Lenz vector. Our approach guarantees not only derivation of Johnson–Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian.

The Randall–Sundrum two-brane model admits the flat-brane Lorentz-invariant vacuum solution only if the branes have exactly opposite tensions. We pay attention to this condition and propose a generalization of this model in which two branes are described by actions of the same form and with the same matter content but with opposite signs. In this way, the relation between their tensions (which are their vacuum energy densities) is naturally accounted for. We study a simple example of such a model in detail. It represents the Randall–Sundrum model supplemented by the Einstein scalar-curvature terms in the actions for the branes. We show that this model is tachyon-free for sufficiently large negative values of the brane cosmological constant, that gravitational forces on the branes are of opposite signs, and that physically most reasonable model of this type is the one where the five-dimensional gravity is localized around the visible brane. The massive gravitational modes in this model have ghost-like character, and we discuss the significance of this fact for the quantum instability of the vacuum on the visible brane.

Using simultaneous shape invariance with respect to two different parameters, we introduce a pair of appropriate operators which realize shape invariance symmetry for the monomials on a half-axis. It leads to the derivation of rotational symmetry and dynamical symmetry group H₄ with infinite-fold degeneracy for the lowest Landau levels. This allows us to represent the Heisenberg–Lie algebra h₄ not only by the lowest Landau levels, but also by their corresponding standard coherent states.

The violation of Lorentz symmetry is studied from the point of view of a canonical formulation. We make the usual analysis on the constraints structure of the Carroll–Field–Jackiw model. In this context we derive the equations of motion for the physical variables and check out the dispersion relations obtained from them. Therefore, by the analysis using Symplectic Projector Method (SPM), we can check the results about this type of Lorentz breaking with those in the recent literature: in this sense we can confirm that the configuration of v^μ space-like is stable, and the v^μ time-like carry tachionic modes.

We consider NSR superstring in AdS₃⊗S³⊗R₄ background. The action is expressed in terms of the variables on the group manifolds SL(2, R) and SU(2) as (1+1)-dimensional σ-models with Wess–Zumino terms, associated with AdS₃ and S³ respectively. R₄ is the flat Euclidean space. We show the existence of classical nonlocal conserved currents in the superspace formulation for the nonlinear σ-model with WZ term in the context of NSR string. We propose Ward identities utilizing existence of the nonlocal conserved currents.

In the context of topcolor-assisted techicolor (TC2) models, we study the lepton flavor violating (LFV) signals of the neutral scalars (the top-pion and the top-Higgs boson) at hadron colliders via considering their contribution to the processes (l = μ or e). We find that the LFV signals of these new particles cannot be detected at the Tevatron with , while might be observable in the future LHC with .