Using Salpeter's propagator for solving the Bethe-Salpeter equation

Bijtebier, J.; Broekaert, Jan

doi:10.1016/s0375-9474(96)00320-x

Cited by 10 publications

(26 citation statements)

References 54 publications

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“…14) 15) where the first term on the right hand side of the above two equations is the projection of each momentum onto the total momentum. The above definition of the relative momentum guarantees the orthogonality of the total momentum and the relative momentum, …”

Section: Hamiltonian Formulation Of the 2-body Problem From Constmentioning

confidence: 99%

“…Much progress has been made in the study of relativistic two-body bound state problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In the 1970s, several authors used Dirac's constraint mechanics [1] to attack the relativistic two-body problem at its classical roots [2], successfully evading the so-call "no interaction theorem" [3].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, from the Bethe-Salpeter equation with this constraint, one can derive [10,7] the "quasipotential equation" of Todorov [9], which is a Schrödinger-like inhomogeneous integral equation where the quasipotential Φ is related to the scattering amplitude in perturbative quantum field theory. Other methods of reducing the Bethe-Salpeter equation have also been suggested [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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RelativisticN-body problem in a separable two-body basis

Wong

Crater

2001

Phys. Rev. C

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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 Hamiltonian is relativistically covariant. It can be easily separated in terms of the center-of-mass and the relative motion of any twobody subsystem. It can also be separated into an unperturbed Hamiltonian with a residual interaction. In a system of two-body composite particles, the solutions of the unperturbed Hamiltonian are relativistic two-body internal states, each of which can be obtained by solving a relativistic Schrödinger-like equation. The resultant two-body wave functions can be used as basis states to evaluate reaction matrix elements in the general N -body problem. 1We prove a relativistic version of the post-prior equivalence which guarantees a unique evaluation of the reaction matrix element, independent of the ways of separating the Hamiltonian into unperturbed and residual interactions.Since an arbitrary reaction matrix element involves composite particles in motion, we show explicitly how such matrix elements can be evaluated in terms of the wave functions of the composite particles and the relevant Lorentz transformations.2

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Section: Hamiltonian Formulation Of the 2-body Problem From Constmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

RelativisticN-body problem in a separable two-body basis

Wong

Crater

2001

Phys. Rev. C

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“…The argument of the δ and the inverse of the propagator should be combinations of the operators used in the free equations (at last approximately and for the positive-energy solutions). Ther exists an infinity of possible combinations [8,12,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. The best choice depends on the quantities one wants to compute (energy of the lowest state, hyperfine splitting, recoil of a nucleus, etc...) and on the properties one wants to preserve exactly in the first approximation (cluster separability, Lorentz invariance, heavy mass limits, charge conjugation symmetry...).…”

Section: Notationsmentioning

confidence: 99%

3D reduction of the three-fermion Bethe-Salpeter equation

Bijtebier

1999

Few-Body Problems in Physics ’98

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“…The Bethe-Salpeter equation [1,2] is the usual tool for computing relativistic bound states [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The principal difficulty of this equation comes from the presence of N-1 (for N particles) unphysical degrees of freedom: the relative time-energy degrees of freedom.…”

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confidence: 99%

Bound state equation for 4 or more relativistic particles

Bijtebier

2002

Nuclear Physics A

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We apply the 3D reduction method we recently proposed for the N-particle Bethe-Salpeter equation to the 4-particle case. We find that the writing of the Bethe-Salpeter equation is not a straightforward task when N is larger or equal to 4, owing to the presence of mutually unconnected interactions, which could lead to an overcounting of some diagrams in the resulting full propagator. We overcome this difficulty in the N=4 case by including three counterterms in the Bethe-Salpeter kernel. The application of our 3D reduction method to the resulting Bethe-Salpeter equation suggests us a modified 3D reduction method, which gives directly the 3D potential, without the need of writing the Bethe-Salpeter kernel explicitly. The modified reduction method is usable for all N.Comment: 16 pages, three figures in one PS file. In this improved version, the writing of the 3D potential is straightforwar

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Using Salpeter's propagator for solving the Bethe-Salpeter equation

Cited by 10 publications

References 54 publications

RelativisticN-body problem in a separable two-body basis

RelativisticN-body problem in a separable two-body basis

3D reduction of the three-fermion Bethe-Salpeter equation

Bound state equation for 4 or more relativistic particles

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