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

Understand

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.