Abstract
We study the relativistic dynamics of a two-body system with nonminimal couplings in the topological defect-generated 1 + 2 -dimensional space–time by using a fully-covariant two-body Dirac equation. We choose the nonminimal couplings as Cornell type interaction potential function and analyze the dynamics of such an interacting fermion-antifermion system (static). The corresponding equation has led 4 × 4 matrix equation, resulting in four first-order equations, two of which are algebraic. We have performed the exact solution of this set of equations and have found an exact spectrum in closed-form. This has given us an opportunity to discuss the effect of space–time background on the dynamics of the considered composite structure. Our findings have shown that all of the possible spin quantum states of such a pair of fermion-antifermion pair sense differently the effect of the space–time background and have shown that the space–time topology impacts on the interaction of such a pair of fermion-antifermion.
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