Related papers: Relativistic potential of a hydrogen-like system i…

Thanks to the Dirac equation, the hydrogen-like atom at high $Z$ offers a precise model of relativistic bound state, allowing to test properties of unpolarized and polarized structure functions analogous to the hadronic ones, in particular:…

A method is presented for constructing a class of Poincare invariant quantum mechanical models of systems of a finite number of degrees of freedom that satisfy cluster separability, the spectral condition, but do not conserve particle…

A new approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main novel feature of this approach is the new…

The new potential model for pionic hydrogen, constructed with the employment of the two-body relativistic equation, is offered. The relativistic equation, based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one, describes the…

We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…

The Poincar\'e (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincar\'e group. The physical laws are formulated in terms of points,…

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals…

In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those…

Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract…

This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…

The methodology based on the association of the Variational Method with Supersymmetric Quantum Mechanics is used to evaluate the energy states of the confined hydrogen atom.

The purpose of the present note is to propose, in the framework of relativistic quantum mechanics, a new Poincare-invariant equation for two particles with masses m_1, m_2 and spin s_1=s_2=1/2. It is a first-order linear differential…

In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…

A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales.…

We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of…

In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…

We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in…

Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…

We present the relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator…

We present a fully covariant transport framework for Molecular Dynamics that enables a consistent description of the evolution of relativistic N-body systems. For the first time, we derive relativistic equations of motion incorporating both…