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The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed…
Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare…
The solvable quantum mechanical model for the relativistic two-body system composed of spin-1/2 and spin-0 particles is constructed. The model includes the oscillator-type interaction through a combination of Lorentz-vector and -tensor…
This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. We…
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a…
With regard to generic two-component systems, the theory of first variations of global quantities is reviewed and explicit expressions are inferred for subsystem potential energies and potential-energy tensors. Performing a conceptual…
We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order…
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…
Appreciating the classical understanding of the elementary particle the "dynamical" Poincare algebra is developed. It is shown that the "dynamical" Poincare algebra and the equations of motion of particles with arbitrary spin are gauge…
The Hamiltonian of the Relativistic Theory of Gravitation (RTG) with nonzero graviton mass is derived. Scalar field is taken as a matter source. The second class constraints are excluded and Dirac brackets are obtained. There are no first…
We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has…
There is no relativistic Hamiltonian for many particles systems except for free particles and this has been accepted since the 1960s from the work of Currie, Jordan and Sudarshan, Cannon and Jordan, and Leutwyler. This is the problem we…
A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a…
We discuss the equivalent form of Levy-Leblond equation [1, 2] such that the nilpotent matrices are two dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1) dimensional Dirac equation.…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement.…
I present a new group-theoretical approach to the interaction mechanism of elementary particle physics. Within an irreducible unitary two-particle representation of the Poincare group, the commutation relations of the Poincare group require…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…