A new method is formulated for calculating the invariant spin field (ISF) at a phase space point by leveraging the property that spins which are distributed along the ISF achieve maximum time-averaged polarization. To quantify this, we construct the time-average of spin rotation matrices beginning at a certain phase space point. It is recognized that the ISF vector at that point achieves the matrix-norm, meaning that the ISF corresponds to the first right-singular vector of that matrix. We show the relation of this method with traditional stroboscopic averaging, such that these methods are two sides of the same coin. This approach offers a new perspective in invariant spin field calculations.
Hamwi et al. (Thu,) studied this question.