Effective field description of vector and tensorial couplings in exotic spinor dynamics: a geometrical approach to Rashba-like interactions

Abstract We investigate the physical consequences of incorporating nontrivial spacetime topology into the dynamics of spinor fields through a geometrical reformulation of exotic spinor structures. By embedding the topological correction directly into the Dirac matrices, we construct an effective framework in which topology manifests as a modification of the spacetime metric and of the associated coupling currents. Within this setting, we derive explicit expressions for the vector and tensorial currents and show that the resulting structure naturally contains a spin-orbit interaction analogous to the Rashba effect. In the non-relativistic limit, the gradient of the topological function plays the role of an effective background field responsible for spin splitting, without the introduction of external electromagnetic interactions. We further analyze the corresponding energy–momentum tensor and demonstrate that the modified dynamics leads to a nontrivial conservation law, which can be interpreted as an effective exchange between the fermionic sector and the topological background. This mechanism gives rise to quasinormal-mode behavior and to birefringent dispersion relations associated with emergent Lorentz-violating effects. Our results establish a direct bridge between exotic spinor geometry, topological structures, and effective spin-orbit and Lorentz-violating phenomena, providing a unified framework that connects geometric topology with observable dynamical consequences.