Relativistic Two-particle System Research Articles

Relativistic Partial Integral Equations for Two-Particle Bound States and the Sturm–Liouville Problem

Bound states of a relativistic two-particle system with arbitrary orbital angular momentum are considered. Three-dimensional integral equations are reduced to partial integral equations and differential equations. Analytical and numerical solutions are presented. The dependences of the spectra of the coupling constant and of the wave functions on various parameters are investigated.

Form factor of a relativistic two-particle system within the relativistic quasipotential approach: Case of an arbitrary masses and a scalar current

A new relativistic form factor for a bound two-particle system was obtained for the case of a scalar current. The respective analysis was performed within the relativistic quasipotential approach based on a covariant Hamiltonian formulation of quantum field theory by going over to a three-dimensional relativistic configuration representation for the case of the interaction of two relativistic spinless particles that have arbitrary masses.

Relativistic two-particle mass spectra from time-asymmetric Fokker action

The relativistic two-particle system with field-type time-asymmetric interactions is considered within the framework of manifestly covariant Hamiltonian formalism with constraints. In the second-order approximation in a coupling constant the mass-shell constraint is presented as a relation between one of the generators of SO(2, 1) and the total mass squared of the system. An algebraic quantization of the classical problem is proposed and the relativistic mass spectra for a wide range of the field-type interactions are obtained.

THE TWO-PARTICLE TIME-ASYMMETRIC RELATIVISTIC MODEL WITH CONFINEMENT INTERACTION AND QUANTIZATION

The relativistic two-particle system with confinement interaction is considered. The quantum-mechanical description of the system is built on the base of classical time-asymmetric model presented in Ref. 1. The mass spectrum and the Regge trajectories are analyzed with the use of continued fraction technique.

Time-asymmetric Fokker-type action and relativistic wave equations

A relativistic two-particle system with an arbitrary linear combination of scalar and vector time-asymmetric Fokker-type interactions in a two-dimensional spacetime is considered within the framework of the front form of dynamics. It is shown that the corresponding mass-shell equation takes the form of a linear relation between the generators of the Lie algebra so(2,1). An algebraic quantization of the system is proposed and a closed form for the mass spectrum is obtained. The relativistic wave equation obtained by Barut and Rasmussen for the H atom is generalized to the case of an arbitrary linear combination of scalar and vector interactions. An extension of the results to the system in four-dimensional spacetime is suggested.

On Relativistic Mass Spectra of a Two-Particle System

A relativistic two-particle system with time-asymmetric scalar and vector interactions in the two-dimensional space-time is considered within the frame of the front form of dynamics using the dynamical symmetry approach. The mass-shell equation may be represented in terms of the nonlinear canonical realization of the Lie algebra of the group SO(2, 1). This allows us to quantize the system and to obtain a closed form for the mass spectrum.

Notes on possible S-wave resonances in relativistic two-particle systems

Some models of relativistic two-particle systems are examined for possible irregularities in the S-wave continuous spectrum. None are found, though we show that with singular effective interaction potentials it is quite easy to run into artificial resonances originating from inaccurate calculations.

A one-dimensional invariance principle for gauge fields of integer spin

A relativistic two-particle system is analyzed in which the particles are bound by an harmonic oscillator potential. The system is invariant under τ-reparametrizations as well as under two gauge transformations of the coordinates. The corresponding first-class constraints give a BRST charge which can be used to construct a classical field theory action for all integer spin gauge fields.

Classical and quantal Einstein relativistic two-particle systems

We present formalisms for the description of two-particle systems of classical and of quantal Einstein relativistic particles. For each case the presentation follows a standard scheme. We define the phase-space, the observables, and the action of the kinematical symmetry group in the center-of-mass representation. We then discuss some of the elementary features of the description of two-particle systems in order to be able to interpret the objects considered. In particular, we show that the description of the free particles conforms to standard relativistic kinematics. As an application we discuss the system consisting of two charged particles interacting via the Coulomb field.

Relativistic potential models as systems with constraints and their interpretation

Recent proposals of classical relativistic two-particle systems with an interaction potential instead of a force field are studied. These are local in an evolution parameter and are formulated as generalized gauge theories within Dirac's formalism for constrained Hamiltonian systems simulating reparametrization invariance. It is shown that the solutions of the equations of motion in general are world sheets instead of world lines. Requiring world lines we derive a set of conditions generalizing the world-line conditions usually given in the literature. Only a limited set of gauge constraints is shown to satisfy these conditions, notably when the evolution parameter is chosen to be the time of the rest frame of the system. A property of this gauge is that the total momentum at laboratory time is in general not just the sum of the momenta of the particles; the missing part is normally viewed as a momentum carried by a force field.

Description of the form factor of a relativistic two-particle system in the covariant Hamiltonian formulation of quantum field theory

Description of the form factor of a relativistic two-particle system in the covariant Hamiltonian formulation of quantum field theory

Relativistic Two-Particle System and Spin-Mass Relations of Meson

Relativistic Two-Particle System and Spin-Mass Relations of Meson

Relative Position Representation for a Relativistic Two-Particle System

Two-particle angular momentum states are constructed which are localized with respect to the magnitude of the relative position in the rest system and which have arbitrary 3-momentum dependence. The associated relative position operator is constructed, and a quantum-mechanical analog of the classical impact parameter is identified. Two-particle angular momentum states are constructed, which are also localized with respect to the ``mean-position'' of the 2-particle system, and the associated ``mean-position'' operator is seen to be a generalization of the 1-particle Newton-Wigner position operator.

Relativistic Particle Dynamics and the S Matrix

Direct-interaction theories are examined from the viewpoint of relativistic scattering theory and the associated concept of ``asymptotic covariance.'' It is pointed out that with any two-particle Hamiltonian which has no bound states there can be associated a variety of representations of the Lie algebra of the inhomogeneous Lorentz group (IHLG), although the S matrix is in general not covariant. It is shown that the requirement of asymptotic covariance ensures both the covariance of the S matrix and the existence of a unique representation of the IHLG to be associated with the relativistic two-particle system. The connection between the Lie algebra, the covariant form of the S matrix, and the uniqueness of K, the generator of pure Lorentz transformations, is thereby clarified. The extension of these considerations to include bound states is made. The form of H given by Bakamjian and Thomas is shown to satisfy asymptotic covariance and, moreover, to be the most general form of interest from the viewpoint of relativistic scattering theory, thereby including as a special case a form of H suggested by Sudarshan. It is also proved that relativistic Hamiltonians of this type do not admit the usual notion of a coupling constant.

Kinematics of the Relativistic Two-Particle System

Knowing the (canonical) forms that the generators of the infinitesimal transformations of P (the restricted Poincaré Group) take when operating within the Hilbert space of states of an arbitrary irreducible representation of P, such as that which affords a kinematic description of a single relativistic particle, we develop the forms in which they appear when operating within the Hilbert space of states of the (reducible) direct product representation of P which describes a system of two non-interacting relativistic particles. On introducing the Clebsch-Gordan (C-G) series of P which expresses the resolution of this latter Hilbert space into a direct integral over the Hilbert spaces wherein operate the irreducible constituents of the direct product representation, we prove that the generators operate in canonical form within each of these subspaces. If we adopt the alternative viewpoint that the C-G series of P must be written exactly so as to achieve this, our analysis may be regarded as providing a fully explicit and mathematically complete derivation of the formula for the C-G coefficients of P that appear in the C-G series. This formula has previously been suggested only on the basis of heuristic physical argument, and its proof is the principal accomplishment of the present work. One important fact which receives further clarification from the explicit nature of our analysis is the following: in order to see how the intrinsic angular momentum of the two-particle system, in a state of given linear momentum, is compounded from the relative angular momentum and intrinsic spins of the particles, one must view the state from a frame of reference wherein it appears to have zero momentum.