Related papers: On a general way of two-particle problem reduction
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
It is shown that an oldest form of variational calculus of mechanics, the Maupertuis least action principle, can be used as a simple and powerful approach for the formulation of the variational principle for damped motions, allowing a…
We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of…
According to the Maupertuis principle, the movement of a classical particle in an external potential $V(x)$ can be understood as the movement in a curved space with the metric $g_{\mu\nu}(x)=2M[V(x)-E]\delta_{\mu\nu}$. We show that the…
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for…
It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…
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…
A quantum version of the action principle is considered in the case of a free relativistic particle. The classical limit of the quantum action is obtained.
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
The open relativistic two-body problem, when two interacting particles also are in external potentials, is considered in terms of the principle of the least action. Based on the consistent modification of the relativistic version Newton's…
We consider two-particle correlations, which appear in relativistic nuclear collisions due to the quantum statistics of identical particles, in the frame of two formalisms: wave-function and current. The first one is based on solution of…
We consider the motion of a spinning relativistic particle with an arbitrary value of spin in external electromagnetic and gravitational fields, to first order in the external field. We use the noncovariant description of spin. An explicit…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
For the electromagnetic interaction of two particles the relativistic quantum mechanics equations are proposed. These equations are solved for the case when one particle has a small mass and moves freely. The initial wave functions are…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…
A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.