The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (spinless case)

Bijtebier, J.; Broekaert, Jan

doi:10.1007/bf02730640

Cited by 21 publications

(26 citation statements)

References 16 publications

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“…According to Grotch and Hegstrom [2], "the BS equation may be minimally coupled provided the external field is time independent. "] It has been carried out for some static external potentials [16]. In that case the results obtained so far agree (at least at first order) with the ansatz (notice that the ansatz produces no extra term at this order for two opposite charges in a constant field).…”

Section: Constant Electric Seldsupporting

confidence: 58%

Pseudomomentum conservation for one-body and two-body relativistic dynamics in a constant electromagnetic field

Droz‐Vincent

1995

Phys. Rev. A

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The pseudomomentum is conserved for a single charge in any constant (over space and time) electromagnetic field. It is also conserved for a neutral two-body system, not only in a pure (constant) magnetic field, but also in a pure (constant) electric field, and explicit wave equations can be written. A neutral two-body system in a constant electric field is treated in a way that parallels our previous approach to this system in a constant magnetic field. Relative motion is separated, but the relative time now survives, whereas a spacelike degree of freedom gets eliminated. In other cases, there is, in general, no evidence of a closed form of the wave equations, but conservation of the pseudomomentum can be required as a reasonable condition for implicitly determining the so-called "three-body terms" in the wave equation.

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Section: Constant Electric Seldsupporting

confidence: 58%

Pseudomomentum conservation for one-body and two-body relativistic dynamics in a constant electromagnetic field

Droz‐Vincent

1995

Phys. Rev. A

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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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“…In this framework the motion is generated by the (half) squared-mass operators and is governed by a system of N coupled wave equations [7][8][9][10][11][12][13]. In the two-body case, the relationship between this approach and the conventional methods of quantum field theory has been established [14,15], [16] 2 . An advantage of the constraint formalism over the Bethe-Salpeter equation is the natural elimination of the relative-time degree of freedom.…”

Section: Introduction Notationmentioning

confidence: 99%

Symmetries of the Relativistic Two-Boson System in External Field

Droz‐Vincent

2009

Int J Theor Phys

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We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external field, when this field is "strongly" translation invariant in some directions and additionally remains unchanged by other isometries of spacetime. Since the relativistic interactions cannot be composed additively, it is not a priori garanteed that the two-body system inherits all the symmetries of the external potential. However, using an ansatz which permits to preserve the compatibility of the mass-shell constraints in the presence of the field, we show how the "surviving isometries" can actually be implemented in the two-body wave equations.

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The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (spinless case)

Cited by 21 publications

References 16 publications

Pseudomomentum conservation for one-body and two-body relativistic dynamics in a constant electromagnetic field

Pseudomomentum conservation for one-body and two-body relativistic dynamics in a constant electromagnetic field

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

Symmetries of the Relativistic Two-Boson System in External Field

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