Relativistic fermions and vector bosons in magnetized three-dimensional space-time with a cosmological constant

In this manuscript, we study the relativistic dynamics of fermions and vector bosons within a (2+1)-dimensional magnetized space-time. We consider the Bonnor-Melvin magnetic space-time, characterized by a homogeneous magnetic field aligned along the symmetry axis and a non-zero cosmological constant. This space-time background, featuring cylindrical symmetry, retains the invariance of quantum field dynamics under Lorentz boosts along the z-direction. This enables us to explore (2+1)-dimensional realms, where the associated 2+1-dimensional spacetime background is recognized as the Bonnor-Melvin magnetic 2+1+0-brane solution within the framework of gravity coupled with nonlinear electrodynamics. We seek exact solutions for relativistic fermions and vector bosons within this space-time background. We have managed to derive the radial wave equations in both instances, securing precise eigenvalue solutions devoid of any approximations. Our findings extend seamlessly to massless fermions and vector bosons, ensuring generality. Moreover, we observe that the ground state energy of massless vector bosons (photons) within the examined space-time background is unequivocally zero.