  The unification of quantum theory and gravity is one of the central open
problems in physics. While most of the effort in the literature is focused on
the UV modifications of quantum theory due to gravity, in this work, we show
that generic infrared (IR) modifications arise when we describe quantum theory
in curved space-time. We explicitly demonstrate that the modifications to the
position-momentum algebra are proportional to the curvature invariants (like
Ricci scalar, Kretschmann scalar). Thus, our results show that infrared effects
in quantum systems do not require any extra assumptions. We study particle
dynamics in an arbitrary curved spacetime by embedding them in a
higher-dimensional flat geometry. Dirac's quantization procedure allows us to
completely capture the dynamics of a particle in 4-dimensional curved spacetime
through the modified position-momentum algebra. We apply the method to a few
spacetimes and show that the corrections due to the space-time curvature are
generic. Furthermore, we compare our results with those derived using extended
uncertainty principles. Finally, we discuss the implications of our work for
black holes and entanglement.
