Speaker
Michele Arzano
Description
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.
