Effective Lagrangian of a bosonic system in a non-trivial topology under magnetic effects

Abstract We investigate a bosonic system within an effective quantum field theory defined on a non-trivial topology in the presence of an external magnetic field. Using the proper-time formalism in the one-loop approximation, we obtain thermal, density, and finite-volume corrections to the effective Lagrangian under spatial confinement. We also analyze the effects of topology and boundary conditions on the system magnetization. Periodic boundary conditions lead to diamagnetic behavior, while antiperiodic boundary conditions induce paramagnetism for the same fixed parameters. Twisted boundary conditions exhibit an intermediate behavior. The analysis is performed within an approximate implementation of the boundary condition in the $$x$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> </mml:math> -direction, where the explicit $$y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>y</mml:mi> </mml:math> -dependence of the corresponding transition function is neglected. Consequently, the numerical investigation is not restricted to exactly flux-quantized torus configurations. In all cases considered, the external magnetic field induces a monotonic enhancement of the magnetization intensity. In the zero-temperature and infinite-volume limits, our results recover Schwinger’s expression for a spinless quantum field in an external magnetic field.