Relativistic Dynamical Localized Wave Packet Theory: Coherence-Structured Scalar Field Dynamics

This work establishes a Lorentz-invariant relativistic scalar extension of the Dynamical Localized Wave Packet Theory (DLWPT) by formulating a deterministic field ontology directly within spacetime. By utilizing a coherence-scaled Lagrangian density, the framework derives equations of motion and energy-momentum structures where physical attributes such as mass, localization, and inertial response emerge from the intrinsic coherence stiffness of the field rather than from independent postulates or point-like particle identities. A central feature of this construction is the natural emergence of preferred momentum and energy scales that act as a dynamical ultraviolet regulator, suppressing arbitrarily high-frequency excitations while strictly maintaining Lorentz covariance. The theory reinterprets the standard wave function as a representation of information density and field coherence conservation, effectively replacing the probabilistic Born rule with a symmetry-driven conservation law. Furthermore, the framework demonstrates a hierarchical structure where reality operates across nested coherence limits, ensuring that the equations reduce smoothly to both non-relativistic DLWPT and conventional Schrödinger dynamics in the appropriate low-energy limits. This formulation positions DLWPT not as a replacement for relativistic field theory, but as a fundamental reinterpretation that links localization stability and dispersion behavior to a deeper, coherence-based geometric substrate.