  The symmetrization postulate and the associated Bose/Fermi (anti)-commutators
for field mode operators are among the pillars on which local quantum field
theory lays its foundations. They ultimately determine the structure of Fock
space and are closely connected with the local properties of the fields and
with the action of symmetry generators on observables and states. We here show
that the quantum field theory describing relativistic particles coupled to
three dimensional Einstein gravity as a topological defect must be constructed
using a deformed algebra of creation and annihilation operators. This reflects
a non-trivial group manifold structure of the classical momentum space and a
modification of the Leibniz rule for the action of symmetry generators governed
by Newton's constant. We outline various arguments suggesting that, at least at
the qualitative level, these three-dimensional results could also apply to real
four-dimensional world thus forcing us to re-think the ordinary multiparticle
structure of quantum field theory and many of the fundamental aspects connected
to it.
