Light-Front Bethe-Salpeter Equation

Abstract

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.

42 pages, 5 figures

References in corpus (2)

• Infinite Nuclear Matter on the Light Front: Nucleon-Nucleon Correlations
• Light-Front Nuclear Physics: Mean Field Theory for Finite Nuclei

Cited by in corpus (49)

• Revealing the structure of light pseudoscalar mesons at the Electron-Ion Collider
• Solving Bethe-Salpeter equation in Minkowski space
• Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics
• Pair term in the Electromagnetic Current within the Front-Form Dynamics: Spin-0 Case
• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane
• Space-like and time-like pion electromagnetic form factor and Fock state components within the Light-Front dynamics
• Skewed quark distribution of the pion in the light-front quark model
• Exploring skewed parton distributions with two body models on the light front II: covariant Bethe-Salpeter approach
• New effective treatment of the light-front nonvalence contribution in timelike exclusive processes
• Higher Fock State Contributions to the Generalized Parton Distribution of Pion
• Continuity of generalized parton distributions for the pion virtual Compton scattering
• Bethe-Salpeter bound-state structure in Minkowski space
• Pion structure in the nuclear medium
• Light-Front projection of spin-1 electromagnetic current and zero-modes
• Observing the Minkowskian dynamics of the pion on the null-plane
• Chiral symmetry and pi-pi scattering in the Covariant Spectator Theory
• Projecting the Bethe-Salpeter Equation onto the Light-Front and back: A Short Review
• Fermionic bound states in Minkowski-space: Light-cone singularities and structure
• Comparison of two Minkowski-space approaches to heavy quarkonia
• Levi-Civita Solutions Coupled with Electromagnetic Fields
• Ground states of the Wick-Cutkosky model using light-front dynamics
• Bound state equation for the Nakanishi weight function
• Light-front Ward-Takahashi Identity for Two-Fermion Systems
• Frame dependence of form factors in light-front dynamics
• Current in the light-front Bethe-Salpeter formalism II: Applications
• Current in the light-front Bethe-Salpeter formalism I: Replacement of non-wave function vertices
• Final state interaction in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ with $K\pi$ I=1/2 and 3/2 channels
• Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the Covariant Spectator Theory
• Three-body bound states with zero-range interaction in the Bethe-Salpeter approach
• The box diagram in Yukawa theory
• Relativistic dynamics of Qqq systems
• Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
• Gauge invariant reduction to the light-front
• Study of the in-medium nucleon electromagnetic form factors using a light-front nucleon wave function combined with the quark-meson coupling model
• Bethe-Salpeter equation in Minkowski space with cross-ladder kernel
• Color-suppression of non-planar diagrams in bosonic bound states
• Proton image and momentum distributions from light-front dynamics
• Zero Mode Effect Generalization for the Electromagnetic Current in the Light Front
• Bethe-Salpeter equation with cross-ladder kernel in Minkowski and Euclidean spaces
• Eletroweak Form Factors in the Light-Front for Spin-1 Particles
• Electromagnetic structure and weak decay of pseudoscalar mesons in a light-front QCD-inspired model
• $B^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$: three-body final state interactions and $K\pi$ isospin states
• Proton quark distributions from a light-front Faddeev-Bethe-Salpeter approach
• Pion inspired by QCD: Nakanishi and Light-Front Integral Representations
• Chiral-symmetry breaking and confinement in Minkowski space
• Light-front projections of the Bethe-Salpeter amplitude and the 4D electromagnetic current for an interacting two-fermion system
• Light-Front Dynamics and Generalized Parton Distributions
• Time-like electromagnetic form factors of $\Lambda ,\Sigma$ and ${\Xi }^{+}$ in a light-front quark model