Group Velocity as an Emergent Quantity from Phase Dispersion

A Structural Interpretation of Wave Packet Propagation Beyond Particle Motion

抄録

Group velocity is commonly introduced as the derivative of angular frequency with respect to wave number.
Although widely used in wave mechanics, optics, and condensed matter physics, its physical interpretation is often conflated with particle velocity or signal propagation speed.
In this paper, we reformulate group velocity as an emergent observable arising from phase dispersion under coherence constraints.
By explicitly deriving group velocity from wave packet construction, we clarify its structural nature and explain why it can differ from particle velocity without violating causality.
This perspective highlights group velocity as an effective quantity determined by phase organization rather than a fundamental dynamical variable.