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The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalise the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using…
Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization…
Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and…
We show that the mutual coherence of a relativistic electron beam in a Coulomb-disordered medium is governed by an effective two-dimensional compact phase field with a logarithmic correlation function. The corresponding Gaussian free-field…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum…
We develop a field theory formalism for the disordered interacting electron liquid in the dynamical Keldysh formulation. This formalism is an alternative to the previously used replica technique. In addition it naturally allows for the…
A model which combines the perturbative behavior of QCD with low energy phenomenology in a unified framework is developed. This is achieved by applying a similarity transformation to the QCD Hamiltonian which removes interactions between…
Non-canonical quantization is based on certain reducible representations of canonical commutation relations. Relativistic formalism for electromagnetic non-canonical quantum fields is introduced. Unitary representations of the Poincar\'e…
This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
Instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at $Z>137/2$ for a spinless boson and at $Z>137$ for electron. Then, focus is concentrated on description of…
In the past five years enormous progress has been made in the ab initio calculations of the optical response of electrons in semiconductors. The calculations include the Coulomb interaction between the excited electron and the hole left…
One way of arriving at a quantum field theory of electrons and positrons is to take a classical theory of the Dirac field and then quantize. Starting with the standard classical field theory and quantizing in the most straightforward way…
We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The…
We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before…
It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric.…
Modification of the right-hand-side of canonical commutation relations (CCR) naturally occurs if one considers a harmonic oscillator with indefinite frequency. Quantization of electromagnetic field by means of such a non-CCR algebra…