Title: Nonperturbative quantum and conformal gravity
Abstract: Loop Quantum Gravity (LQG) and Spin Foam (SF) models are an
attempt at a diffeomorphism invariant or non-perturbative formulation
of quantum gravity. In the first part of this talk we will present an
introduction to LQG and the SF models beginning by a brief motivation,
reviewing the method of Dirac constraint quantization and applying it
to the Holst action, thus obtaining LQG. We will then quickly skim over
the main results that this formulation of quantum gravity has obtained
so far, some of its most important open questions and introduce the SF
models that are an attempt at a path integral formulation of LQG.
We shall also review the main results of the SF approach as well as
some of its main open questions.
In the second half of the talk, we will look more in detail at the
twistor formulation of the SF models. Especially introducing the
twisted geometry of the spinnetworks, a 3d quantum polyhedral geometry
with a discontinuous metric. Spin networks are the states between which
the transition amplitudes are calculated in the SF approach to quantum
gravity and the kinematical states of the LQG approach. We shall then
motivate the interest in conformally invariant theories and sketch how
the spinnetworks should be generalizable to this setting
(a work in progress).