  This paper presents a new non-associative algebra which is used to (i) show
how the spectator (or Gross) two-body equations and electromagnetic currents
can be formally derived from the Bethe-Salpeter equation and currents if both
are treated to all orders, (ii) obtain explicit expressions for the Gross
two-body electromagnetic currents valid to any order, and (iii) prove that the
currents so derived are exactly gauge invariant when truncated consistently to
any finite order. In addition to presenting these new results, this work
complements and extends previous treatments based largely on the analysis of
sums of Feynman diagrams.

Nuclear Theory