Light-front Ward-Takahashi Identity for Two-Fermion Systems

Abstract

We propose a three-dimensional electromagnetic current operator within light-front dynamics that satisfies a light-front Ward-Takahashi identity for two-fermion systems. The light-front current operator is obtained by a quasi-potential reduction of the four-dimensional current operator and acts on the light-front valence component of bound or scattering states. A relation between the light-front valence wave function and the four-dimensional Bethe-Salpeter amplitude both for bound or scattering states is also derived, such that the matrix elements of the four-dimensional current operator can be fully recovered from the corresponding light-front ones. The light-front current operator can be perturbatively calculated through a quasi-potential expansion, and the divergence of the proposed current satisfies a Ward-Takahashi identity at any given order of the expansion. In the quasi-potential expansion the instantaneous terms of the fermion propagator are accounted for by the effective interaction and two-body currents. We exemplify our theoretical construction in the Yukawa model in the ladder approximation, investigating in detail the current operator at the lowest nontrivial order of the quasi-potential expansion of the Bethe-Salpeter equation. The explicit realization of the light-front form of the Ward-Takahashi identity is verified. We also show the relevance of instantaneous terms and of the pair contribution to the two-body current and the Ward-Takahashi identity.

48 pages, 3 figures

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Cited by in corpus (15)

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• Light-Front projection of spin-1 electromagnetic current and zero-modes
• Projecting the Bethe-Salpeter Equation onto the Light-Front and back: A Short Review
• Observing the Minkowskian dynamics of the pion on the null-plane
• Fermionic bound states in Minkowski-space: Light-cone singularities and structure
• Two-particle twist-3 distribution amplitudes of the pion and kaon in the light-front quark model
• Light-Front spin-dependent Spectral Function and Nucleon Momentum Distributions for a Three-Body System
• Final state interaction in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ with $K\pi$ I=1/2 and 3/2 channels
• Distorted spin-dependent spectral function of an A=3 nucleus and semi-inclusive deep inelastic scattering processes
• Light-Front Model of Transition Form-Factors in Heavy Meson Decay
• Ward-Takahashi identity in the light-front formalism for a bound state of fermions
• Pion electromagnetic form factor with Minkowskian dynamics
• Light-front projections of the Bethe-Salpeter amplitude and the 4D electromagnetic current for an interacting two-fermion system