Derivation of a 4D Quantum Potential in Flat Minkowski Space

We derive a fully covariant four-dimensional quantum potential in flat Minkowski space, extending the non-relativistic de Broglie–Bohm framework. Starting from the Klein–Gordon equation, we express the scalar field in polar form and systematically obtain a quantum correction term that generalizes the three-dimensional quantum potential. This 4D potential, emerging naturally from the relativistic dynamics, maintains Lorentz invariance and reduces to the familiar non-relativistic form in the appropriate limit. Our approach demonstrates a first-principles derivation without a priori assumptions about its form, offering a foundation for further exploration of quantum-relativistic interactions in flat spacetime.