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Light-front Ward-Takahashi Identity for Two-Fermion Systems | | J. A. O. Marinho
; T. Frederico
; E. Pace
; G. Salme’
; P. Sauer
; | | Date: |
6 May 2008 | | 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. | | Source: | arXiv, 0805.0707 | | Services: | Forum | Review | PDF | Favorites | |
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