We introduce a relativistic complex scalar field model motivated by the Information Discrimination Theory (IDT) framework, in which the field amplitude is interpreted as a local measure of configuration distinguishability. The theory is defined by a Lorentz-invariant Lagrangian with a nonlinear self-interaction potential that supports spontaneous symmetry breaking and admits spatially localized, finite-energy solutions. For a spherically symmetric stationary ansatz, the field equations reduce to a nonlinear radial boundary-value problem; we demonstrate that the model naturally yields particle-like solitonic configurations (spin-0 excitations) characterized by a rest energy obtained from the corresponding Hamiltonian functional. Classical stability of these solitons is established using the Vakhitov–Kolokolov criterion, and absolute stability against decay (via E/Q<m0) is confirmed for approximately 58% of the frequency existence window; the remaining 42% are energetically unstable and excluded from dark matter candidacy. We further couple the scalar to an Abelian gauge field via minimal coupling and demonstrate how symmetry breaking generates a gauge-boson mass term within this framework. The absolutely stable solitonic configurations represent viable candidates for scalar dark matter in the microscopic mass regime; macroscopic masses require gravitationally bound boson star extensions. We establish a connection between the kinetic structure and Fisher information geometry, and propose extensions to fermionic matter via Yukawa coupling. The relationship to established non-topological soliton (Q-ball) literature is discussed, along with explicit limitations of the present model and directions for extension. While the IDT interpretation provides conceptual motivation, the main results—the existence of absolutely stable localized solutions, their dark matter phenomenology, and symmetry-breaking dynamics—stand independently as contributions to nonlinear field theory.
Mahgoub Salih (Wed,) studied this question.