Spectral and projection properties of “two-time” Green's functions of $n$ particles in null-plane quantum field theory

A spectral representation with respect to the square of the total four-momentum is obtained for the “two-time” Green's function of $n$ particles of arbitrary spin in nullplane quantum field theory. The projection properties of the two-time Green's functions and the corresponding wave functions with respect to the scaled variable $\eta_i=p_i{^+}/P^+$ and also the spin structure are investigated. The transformation properties of the quasipotential variables under Lorentz rotations in the $x^0$, $x^3$ plane and shifts in the space of the transverse momenta of the particles are examined. Three-dimensional equations are obtained for the complete description of a system of three particles of arbitrary spin.