Related papers: Superintegrable relativistic systems in spacetime-…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
Cylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them…
We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The…
We inquire into classical and quantum laws of motion for the point charge sources in the nonlinear Maxwell-Born-Infeld field equations of classical electromagnetism in flat and curved Einstein spacetimes.
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically…
The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…
We construct an additional independent integral of motion for a class of three dimensional minimally superintegrable systems with constant magnetic field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages]…
In this paper the physical systems consisting of relatively moving subsystems are considered in the "true transformations relativity." It is found in a manifestly covariant way that there is a second-order electric field outside stationary…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…
Through their respective sigma models, a bosonic string and a superstring can be coupled to (super)gravity fields. These are subsequently forced to satisfy their right classical equation of motions, as a consequence of quantization of the…
We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the…
Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
We briefly review models of relativistic particles with spin. Departing from the oldest attempts to describe the spin within the lagrangian framework we pass through various non supersymmetric models. Then the component and superfield…