Quantum effective potential from discarded degrees of freedom

I obtain the quantum correction Delta V-eff = (h(2)/8m)[(1 - 4 xi d+1/d)(S')(2) + 2(1 - 4 xi)S ''] that appears in the effective potential whenever a compact d-dimensional subspace (of volume alpha exp[S(chi)]) is discarded from the configuration space of a nonrelativistic particle of mass m and curvature coupling parameter xi. This correction gives rise to a force -(Delta V'(eff)) that pushes the expectation value (chi) off its classical trajectory. Because Delta V-eff does not depend on the details of the discarded subspace, these results constitute a generic model of the quantum effect of discarded variables with maximum entropy/information capacity S(chi). (C) 2018 Elsevier B.V. All rights reserved.