Is there a set of two-body Klein–Gordon equations analogous to the two-body Dirac equations? The classical relativistic constraints analogous to the quantum two-body Dirac equations (discussed in the introduction) and that have the same structure as the above Klein–Gordon one-body form are H 1 = ( p 1 − − A 1 ) 2 + ( m 1 + S 1 ) 2 = p 1 2 + m 1 2 + Φ Φ 1 ≈ ≈ 0 H 2 = ( p 1 − − A 2 ) 2 + ( m 2 + S 2 ) 2 = p 2 2 + m 2 2 + Φ Φ 2 ≈ ≈ 0 , p 1 = ε ε 1 P ^ ^ + p ; p 2 = ε ε 2 P ^ ^ − − p . Defining structures that display time-like vector and scalar interactions π π 1 = p 1 − − A 1 = [ P ^ ^ ( ε ε 1 − − A 1 ) + p ] , π π 2 = p 2 − − A 2 = [ P ^ ^ ( ε ε 2 − − A 1 ) − − p ] , M 1 = m 1 + S 1 , M 2 = m 2 + S 2 , gives H 1 = π π 1 2 + M 1 2 , H 2 = π π 2 2 + M 2 2 . Imposing Φ Φ 1 = Φ Φ 2 ≡ ≡ Φ Φ ( x ⊥ ⊥ ) = − − 2 p 1 ⋅ ⋅ A 1 + A 1 2 + 2 m 1 S 1 + S 1 2 = − − 2 p 2 ⋅ ⋅ A 2 + A 2 2 + 2 m 2 S 2 + S 2 2 = 2 ε ε w A − − A 2 + 2 m w S + S 2 , and using the constraint P ⋅ ⋅ p ≈ ≈ 0 , reproduces Eqs.(12) provided