Light-front Ward-Takahashi identity and current conservation

Abstract

We construct a conserved electromagnetic current for two-boson systems in finite mass boson exchange models within light-front dynamics. For that purpose, we use a quasipotential reduction to perform the three-dimensional light-front projection of the 4-dimensional current operator. The electromagnetic current operator acting on the valence component of bound and scattering states can be perturbatively calculated in the quasipotential expansion, in correspondence with a truncation of the Fock space. The divergence of the proposed current operator satisfies a Ward-Takahashi identity at any given order of the quasipotential expansion. Also shown is the relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter amplitudes and current for bound and scattering states with the 4dimensional ones. The matrix elements of the 4-dimensional current operator can be fully recovered from the corresponding light-front ones. In one test case the theoretical framework is realized explicitly.

Covariance for electromagnetic current for two bosons at higher order in the light front

“…The calculation is considered only in the region 0 < k + 2 < k + i < k + 4 < k + f and its combinations. The same result is found in the article by Marinho, Frederico and Sauer [5], using a different technique.…”

“…We obtained more diagrams than it was considered in a recent article [5], just those in which antiparticles appear. The "Z-graph" appears naturally in our approach.…”

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

“…One may wonder how the valence wave function be able to generate the whole physical complexity of the full BS amplitude. Indeed, within a non perturbative framework, it formally turns out [24][25][26][27][28][29] that by introducing the pro-jection onto the null-plane, namely the analytic integration over the variable k − = k 0 − k 3 , the full BS amplitude can be expressed in terms of the valence component and an operator, producing the richness of the Fock states on top of the lowest one. It must be emphasized that such a result has been obtained for both bound and scattering states of bosonic and fermionic systems.…”

Final state interaction in D + → K − π + π + with Kπ I = 1/2 and 3/2 channels

“…[31] based on the quasi-potential approach (QPA). The reduced amplitudes derived using the tools developed in a series of works [31][32][33][34][35] and reviewed in [36], depends only three-dimensional variables, namely, the kinematical LF momentum k ≡ (k + , k ⊥ ), defined by k + = k 0 + k 3 and k ⊥ = {k x , k y }. The phase-space integration is normalized according to dk…”

“…We use a parametrization of the Kπ scattering amplitude in I = 1/2 and 3/2, which is input to the bachelor integral equations, and constitutes one source of the energy dependence seen in the D + → K − π + π + S-wave phase shift, besides the phase of the Kπ amplitude. Technically, we perform the light-front projection of the equations [31][32][33][34][35][36][37], to simplify the numerical computation of the observables by three-dimensional integrations. These techniques are well exemplified in the reviews of applications of light-front field theory to nuclear and hadron physics [38,39].…”