QED based two-body Dirac equation

Mandelzweig, V. B.; Wallace, S.J.

doi:10.1016/0370-2693(87)91035-5

Cited by 77 publications

(94 citation statements)

References 10 publications

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“…However, one meets here the known difficulty of the "continuum dissolution" problem [24,25], which prevents the existence of normalizable states. Usually, this difficulty is circumvented by the introduction of projection operators, either in the potential [26,27] or in the kinetic terms [4]. It is not yet known whether some local generalization of the Breit equation may avoid the above difficulty.…”

Section: Resultsmentioning

confidence: 99%

How to obtain a covariant Breit type equation from relativistic constraint theory

Mourad¹,

Sazdjian²

1995

J. Phys. G: Nucl. Part. Phys.

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Section: Resultsmentioning

confidence: 99%

How to obtain a covariant Breit type equation from relativistic constraint theory

Mourad¹,

Sazdjian²

1995

J. Phys. G: Nucl. Part. Phys.

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“…(16), the lower components χ can be directly obtained from the solution by using Eqs. (9) and (11). The relevant point for the present study is that the previous equation (obtained with the special condition of Eq.…”

Section: The Dirac Equation With a Special Combination Of Potentialsmentioning

confidence: 93%

“…Note that our quadratic model also gives the two signs of the energy that, as shown in [12], are related to the propagation of (++) and (−−) fermionic states. In that equation, the (+−) and (−+) states are completely suppressed, while, in another (similar) relativistic model [11], they only appear as closed-channel, virtual states. In this way, our equation and the two models cited above do not admit spurious solutions with M = 0, avoiding the socalled continuum dissolution problem, discussed, for example, in Ref.…”

Section: The Two-body Equal-mass Quadratic Equationmentioning

confidence: 97%

“…Some examples are given in Refs. [9][10][11][12][13][14]. Obviously, for a given relativistic equation, the physical results strictly depend on the choice of the quasipotential that represents the interaction.…”

Section: The Two-body Equal-mass Quadratic Equationmentioning

confidence: 99%

“…Our procedure essentially consists in writing the free equation for the relative momentum, total energy and constituent mass of the system, then inserting the scalar and vector interactions by means of standard minimal substitutions. Our model is compared with more standard approaches based on three-dimensional reductions of the BetheSalpeter Equation (BSE) [9][10][11][12][13][14] and to a very complex procedure based on two-body Dirac equations of constraint dynamics [15]. Two generalizations are introduced in Section 4; in Subsection 4.1 a covariant version of the equation for the study of bound systems in any reference frame is proposed; in Subsection 4.2 the equation is also generalized to the case of two constituents with different mass.…”

Section: Introductionmentioning

confidence: 99%

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A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

Sanctis

2014

Open Physics

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Abstract:We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame.A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data. PACS

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Relativistic Three-Particle Dynamical Equations I. Theoretical Development

Adhikari¹,

Frederico²,

Tomio³

1994

Annals of Physics

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Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic unitarity and covariance, first derived by Weinberg and by Blankenbecler and Sugar.These two-particle equations are shown to be related by a transformation of variables.Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and covariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The threeparticle equations we derive are very practical and suitable for performing relativistic scattering calculations.

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QED based two-body Dirac equation

Cited by 77 publications

References 10 publications

How to obtain a covariant Breit type equation from relativistic constraint theory

How to obtain a covariant Breit type equation from relativistic constraint theory

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

Relativistic Three-Particle Dynamical Equations I. Theoretical Development

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