Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Light Cone: Relativistic Nuclear and Particle Physics (LC)

Next-to-leading order light-front three-body dynamics

T. Frederico

Published Mar 9, 2009• 7 citations
Publisher

Abstract

The quasi-potential approach is used to project a four-dimensional field-theoretical model of a three-particle system to the light-front (LF) valence sect or. The starting point is the Bethe-Salpeter equation (BSE) for three particles in the ladder approximation. The projection technique allows to eliminate three-body reducible diagrams from the kernel of the LF integral equation for the valence wave function. We construct the next-to-leading order contribution to the kernel of the LF three-body integral equation. We exemplify the method for a three-boson system with a contact interaction.

DOI
10.22323/1.061.0036

Related papers

Recent developments in light-front dynamics

Vladimir A. Karmanov

Abstract. Recent results on relativistic few body systems, obtained in the framework of light-front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero-range interaction; many-body contributions.

•Jan 1, 2004•0 citations

Three-body bound states with zero-range interaction in the Bethe–Salpeter approach

E. Ydrefors, J. H. Alvarenga Nogueira, Vitor Gigante +2 more

The Bethe–Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe–Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ( i ) For weak enough two-body interaction the three-body system is unbound. ( ii ) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ( iii ) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe–Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.

arXiv:1703.07981•Physics Letters B•Apr 20, 2017•14 citations

Recent developments in light-front dynamics

Vladimir A. Karmanov

Recent results on relativistic few body systems, obtained in the framework of light‐front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero‐range interaction; many‐body contributions.

arXiv:nucl-th/0410033•AIP conference proceedings•Jan 1, 2005•0 citations

Ladder equation for the three-particle vertex and its approximate solution

Patrick Kappl, T. Ribic, Anna Kauch +1 more

We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducible vertices, each connecting two fermionic lines. The comparison to the exact solution shows that this approximation is only good for rather weak interactions and even then only qualitatively—at least for the nonlinear response function analyzed.

arXiv:2412.01848•Physical Review Research•Sep 10, 2025•0 citations

A light-front coupled-cluster method for quantum field theories

John R. Hiller

The Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the standard coupled-cluster method.This approximation eliminates any need for the usual approximation of Fock-space truncation.Instead, the exponential operator is truncated and the terms retained are determined by a set of nonlinear integral equations.These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small.Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory.

arXiv:1206.6057•International Conference on Quarks and Nuclear Physics (QNP)•Oct 1, 2012•1 citation

A nonperturbative light-front coupled-cluster method

John R. Hiller

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.

arXiv:1208.6077•AIP conference proceedings•Jan 1, 2012•1 citation
The quasi-potential approach is used to project a four-dimensional field-theoretical model of a three-particle system to the light-front (LF) valence sect or. The starting point is the Bethe-Salpeter equation (BSE) for three particles in the ladder approximation. The projection technique allows to eliminate three-body reducible diagrams from the kernel of the LF integral equation for the valence wave function. We construct the next-to-leading order contribution to the kernel of the LF three-body integral equation. We exemplify the method for a three-boson system with a contact interaction.
The Bethe–Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe–Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ( i ) For weak enough two-body interaction the three-body system is unbound. ( ii ) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ( iii ) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe–Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.
We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducible vertices, each connecting two fermionic lines. The comparison to the exact solution shows that this approximation is only good for rather weak interactions and even then only qualitatively—at least for the nonlinear response function analyzed.
The Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the standard coupled-cluster method.This approximation eliminates any need for the usual approximation of Fock-space truncation.Instead, the exponential operator is truncated and the terms retained are determined by a set of nonlinear integral equations.These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small.Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory.
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.