Constrained Classical Trajectories with Fixed Symplectic Area

Abstract

We study finite bundles of $N$ classical trajectories subject to a fixed symplectic-area condition on their phase-space covariance. We derive constraint forces that preserve this condition with zero bundle-averaged power. Setting $κ= \hbar^2/4$ fixes only the area scale: the trajectories remain classical, and the finite bundle need not be Gaussian. In the Gaussian large-$N$ limit, the centroid and width equations coincide with those of variational Gaussian wave-packet dynamics. Here $N$ specifies the finite-bundle representation, not an order in the Moyal expansion or in an $\hbar$ expansion.