on nonperturbative and relativistic corrections to the highly resonant hadronic bound states

In this article, we suggest a method for calculating the mass spectrum of a bound state with relativistic corrections. in standard calculations of mass spectra that consider the nonperturbative nature of interactions, researchers typically consider only the lowest-order term in v/c, the ratio of a particle's velocity inside the bound state to the speed of light. using a theoretical framework based on specific mathematical techniques, we go beyond the lowest-order term in v/c approximation and define the structure of relativistic nonperturbative interaction potential by summing an infinite series in powers of v/c. furthermore, we introduce and characterize a relativistic mass correction formulated through the current-current correlated tensor associated with two charged scalar particles in an external gauge field, where the fields obey gaussian statistics. this two-point correlation function describes the correlation of polarization function components of the current across different spacetime points in a 4d euclidean spacetime coordinate frame. under relativistic conditions, this correlation structure contributes to the formation of bound states, which provide a basis for defining the constituent or relativistic mass of the particle in the bound state. our analysis is carried out within the frameworks of quantum field theory and quantum mechanics.