Approximation and analytical study of the relativistic confined two particles state within the complex potential in the isotropic medium

We have studied the dissociation of particle-antiparticle confined systems through a complex potential, which comes from adjusting and correcting both the perturbative and nonperturbative terms at finite temperatures. The real component of the confining nonperturbative potential makes the bound state stronger; in contrast, the absolute value of the imaginary component contributes more significantly to the thermal width at higher temperatures. The results are presented using the relativistic Bethe-Salpeter equation for the real and imaginary parts of the given potential within the framework of the asymptotic pattern and characteristics of the real and imaginary-time Green’s functions of the bound state as charged particles that couple to a gauge field in any external field. The relativistic behavior of interaction within the Sturmian representation for two intertwined spaces was extracted based on the mathematical quantum field theory technique in the perturbative calculation of the quantum field theory. The expectation value of the vacuum of field operators is defined as a sum of operator product expansion methods. The results are applied to predict the masses of the charmonium confined state and study the heat dynamics and attributes of the system. The expectation values agree with the experimental and theoretical data found within scholarly works and among academic researchers.

Keywords:

Real and imaginary potential , Thermal Properties , Schrödinger equation