相关论文: Comment on ``Kepler problem in Dirac theory for a …

The existence of elliptic periodic solutions of a perturbed Kepler problem is proved. The equations are in the plane and the perturbation depends periodically on time. The proof is based on a local description of the symplectic group in two…

Due to some current interest in this subject we have produced this note. There is no claim to anything new, except possibly to show that a direct numerical approach is quite simple and instructive. For comparison purposes we include a…

Keller's theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem…

The planar quantum dynamics of a neutral particle with a magnetic dipole moment in the presence of electric and magnetic fields is considered. The criteria to establish the planar dynamics reveal that the resulting nonrelativistic…

It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…

This is the third article in a series of four articles dealing with the P vs. NP question. The purpose of this work is to demonstrate that the methods used in the first two articles of this series are not affected by oracle relativizations.…

We argue that the hierarchy problem of the standard model of particle physics can be solved by adding a state-dependent term to the Higgs sector. We present an example of a scalar field with a Higgs-like potential with an additional term…

The existence of radial solutions of a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity…

We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a…

It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…

The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.

We study the electromagnetic fields of an arbitrarily moving charged particle and the radiation reaction on the charged particle using a novel approach. We first show that the fields of an arbitrarily moving charged particle in an inertial…

The characteristic feature of the Kepler Problem is the existence of the so-called Laplace--Runge--Lenz vector which enables a very simple discussion of the properties of the orbit for the problem. It is found that there are many classes of…

A description of elementary particles should be based on irreducible representations of the Poincar\'e group. In the theory of massive representations of the full Poincar\'e group there are essentially four different cases. One of them…

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…

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…

We consider the Cauchy problem of the three-dimensional parabolic-elliptic Patlak-Keller-Segel chemotactic model. The initial data is almost a Dirac measure supported on a straight line with mass less than $8\pi$. We prove that if the data…

Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…

The binding and trapping of particles usually rely on conservative forces, described by unitary quantum dynamics. We show that both can also arise solely from spatially dependent dephasing, the simplest type of decoherence. This can be…

We study the dynamics of a kink in a one-lane asymmetric simple exclusion process with detachment and attachment of the particle at arbitrary sites. For a system with one site of detachment and attachment we find that the kink is trapped by…