Dynamic Doppler Effects on Dirac Spinor Fields

Abstract

We derive the dynamic Doppler effects of noninertial observer motion on Dirac spinor fields, characterizing how proper acceleration, proper jerk, observer path curvature, torsion, and hyper-torsion modify the inertial quantum description of free particles. We quantify the nonlinear behavior of the amplitude and phase of the Dirac spinor wave field and isolate the spin-induced signatures that have no counterpart in the scalar Klein-Gordon field. For worldlines with constant proper jerk the amplitude scales super-exponentially as $\exp(j_0τ^2/4)$. The complex Frenet-Serret curvature invariants generate both an exponential amplitude factor and a spin-induced phase factor. Spinor structure therefore produces an observable dynamic Doppler signature distinct from any scalar prediction.