Relativistic wave equations of combined particles and antiparticles in scalar quantum field theory

Study of virtual annihilation and retardation effects in relativistic two-, four-, and six-body wave equations in scalar QFT

“…[6] simple trial states have been employed to obtain the n-body wave equations in the scalar QFT by the variation method. Thereupon, one can easily write the relativistic wave equations for the two-, four-, and six-body systems.…”

“…One should note that since we are studying here the two-, four-, and six-body systems the total number of particles and antiparticles in the present paper is even. We have for (n/2) particles and (n/2) antiparticles the following simple trial state [6]: where G is normalizable to unity and it should be a wellbehaved function with adjustable parameters. The matrix element for the rest-plus-kinetic energy of the n-body system is…”

“…Even indices are considered for antiparticles and odd indices are considered for particles. The relativistic n-body wave equation for scalar particles-antiparticles can be obtained from the matrix elements as below [6] (for j\kÞ:…”

“…The matrix element for the interaction related to our nbody wave equations (retardation effects are included) is [6] (for j\k):…”

“…In previous works by EmamiRazavi [5,6], it has been demonstrated that, by employing a reformulated model in QFT proposed by Darewych [7,8], formulas concerning relativistic n-body wave equations for scalar particles and/or antiparticles can be obtained (see also [9]). It has also been proven that using Darewych's formalism [7,8] relativistic n-fermion wave equations (particles and antiparticles; spin-1/2) in quantum electrodynamics can be obtained [10,11].…”