Dynamical Mass Generation and Geodesic Modifications from Topological Solitons in q-Deformed Effective Field Theory

We extend the q-deformed Effective Field Theory (q-EFT) framework to investigate tworelated consequences of nonlinear constitutive coupling in the topological background sec-tor. First, we show that the self-interaction of the background 1-form field γµ with thenetwork current Jµ induces a dynamically generated effective mass, producing longitudinaltrace modes in regions of non-vanishing phase gradients. Second, we construct stationarytopological soliton configurations of γµ, characterized by a non-trivial winding number W,and compute the associated energy-momentum tensor. We show that such localized config-urations contribute an effective rest-mass density to the stress-energy tensor, and derive theleading-order geodesic correction induced by the soliton’s effective potential on test-particletrajectories. All results are presented within the weak-field, spherically symmetric approxi-mation; strong-field extensions remain open problems.