  Generalized uncertainty principles (GUP) and, independently, Lorentz symmetry
violations are two common features in many candidate theories of quantum
gravity. Despite that, the overlap between both has received limited attention
so far. In this brief paper, we carry out further investigations on this topic.
At the nonrelativistic level and in the realm of commutative spacetime
coordinates, a large class of both isotropic and anisotropic GUP models is
shown to produce signals experimentally indistinguishable from those predicted
by the Standard Model Extension (SME), the common framework for studying
Lorentz-violating phenomena beyond the Standard Model. This identification is
used to constrain GUP models using current limits on SME coefficients. In
particular, bounds on isotropic GUP models are improved by a factor of $10^{7}$
compared to current spectroscopic bounds and anisotropic models are constrained
for the first time.
