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The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear…
In the present communication the Bayesian conditional probability approach is applied to the wave function of a many-electron system that results in appearance of a quantum vector potential in the DFT Schrodinger equation due to electron…
Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of…
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control.…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
It is shown that the dynamical observables calculated with the point form relativistic quantum mechanics incorporate effects of particle-antiparticle creation from the vacuum by interactions. The electromagnetic observables obtained with…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
The electron attachment variant of equation-of-motion coupled-cluster theory (EOM-EA-CC) is generalized to the case of strong light-matter coupling within the framework of cavity quantum electrodynamics (QED). The resulting EOM-EA-QED-CC…
A century of coherent experimental and theoretical investigations have uncovered the laws of nature that underly nuclear physics. The standard model of strong and electroweak interactions, with its modest number of input parameters,…
We outline a rigorous method which can be used to solve the many-body Schroedinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the…
This paper presents a realistic model that describes radiation-matter interactions. This is achieved by a generalization of first quantization, where the Maxwell equations are interpreted as the electromagnetic component of the Schroedinger…
An overview on the relativistic Dirac-Brueckner approach to the nuclear many-body problem is given. Different approximation schemes are discussed, with particular emphasis on the nuclear self-energy and the saturation mechanism of nuclear…
Reliable calculations of the structure of heavy elements are crucial to address fundamental science questions such as the origin of the elements in the universe. Applications relevant for energy production, medicine, or national security…
The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly…
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows…
We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit,…
We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove…
Soon after the postulation of quarks by Gell-Mann, Zweig and Fritzsch the experimental confirmation of these sub-nucleon formations, Feynman, Ravndal and Kislinger proposed a relativistic three-quark model of the nucleon to study its…
In this paper we start from the Schr\"odinger equation to revisit some classical quantum mechanics from the perspective of phase transition process. Here the relativistic effect of particles moving at high speed can be regarded as the phase…