Finite continuum quasi distributions from lattice QCD

We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via perturbation theory.

A nonperturbative method for the Yang–Mills Lagrangian

Using the properties of the partition function for a Yang–Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.

Polarizability and hyperpolarizability of Li+ calculated from the DC-Stark shift

We show how energy shifts induced by DC fields can be used to obtain the polarizability α and the hyperpolarizability γ of the Lithium cation efficiently. We employ a nonperturbative method to solve a complex eigenvalue matrix equation constructed in terms of two separately optimized function spaces, Q and P. The values obtained for α and γ are in excellent agreement with other elaborate theoretical calculations. PACS Nos.: 02.70.–c, 32.10.Dk, 32.60.+i, 42.65.An

Correlations in many electron systems: theory and applications

In this contribution, we present calculations performed for interacting electron systems within a nonperturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is feasible and planned. The theory is based on the unitary operator eiS (S is the correlation operator) formalism which, in this paper, is treated non perturbatively within many-particle correlations. The application of the derived equations to few-body systems is realized in terms of generalized linearization approximations and via the cluster factorization theory. To check the reliability of the model, we present two different applications. In the first, we evaluate the transitions energies in helium-, lithium-, beryllium-, and boron-like oxygen. The calculation aims for a precise determination of the satellite transitions that play an important role in plasma diagnostics. In the second application we investigate a nonperturbative method to evaluate the charge radii of the helium and lithium isotopes by using the isotopic shift theory. We found that our model leads naturally to components of e––e+ pair in the two-electron wave functions of the helium isotopes and three-electron wave functions of the lithium isotopes. The possible connection of these terms to the quantum electrodynamics leading diagrams is postulated.PACS Nos.: 31.10.+z, 31.30.Gs, 32.30.–r

III. Geometrical optics of variable-frequency light rays in the general relativistic regime: Combined gravitational and refractive lensing

The frequency-sensitive extremum principle for propagation of light rays in the geometrical optics regime is used to develop a nonperturbative method for tracing light rays in a transparent refractive medium in the general relativistic environment. The general formulation of the theory is given first; it allows for the numerical analysis of a nonlinear superposition of gravitational and refractive lensing, when neither of the two effects can be treated as a small perturbation. The scope of the general theory is gradually narrowed to the Schwarzschild field, the spherical symmetry of the refractive properties of the medium, and the small deflection regime approximation. A simple, analytically solvable example of deflection of light rays by a mass embedded in a refractive medium is considered in detail; in a vacuum, deflection of light rays by the Sun is reproduced.PACS Nos.: 42.15-i, 04.20-q, 98.90+s