Non-local currents and their associated conserved 
charges have been known and studied widely in two-
dimensional  field theories. Their main feature is that 
their action on product of fields  is non-additive i.e. it 
follows a "deformed" Leibniz rule.  Less appreciated is 
the fact that non-local charges appear in the context
of three-dimensional Einstein gravity where they 
describe the energy-momentum of a "topologically" 
gravitating point  particle.  Here momenta are Lorentz 
group elements and the non-additive action is
simply a consequence of the non-abelian structure of the 
group.  After a brief introduction I will show how 
quantization of such relativistic point particle with group-
valued momenta leads to a non-commutative
field theory.  As an application I will introduce a non-
commutative heat-kernel, calculate the associated 
spectral dimension and comment on its non-trivial 
behaviour.  Finally I will discuss how these structure can 
be extended to a 4d context and comment on some
potential applications.