Quantum Gravity

The scaling analysis in the large spin limit of Feynman amplitudes for the Bosonic colored group field theory are considered in any dimension starting with dimension 4. By an explicit integration of two colors, we show that the model is positive. This formulation could be useful for the constructive analysis of this type of models.

After implementing an effective minimal length, we will present a new class of spacetimes, describing both neutral and charged black holes. As a result, we will improve the conventional Schwarzschild and Reisner-Nordstroem spacetimes, smearing out their singularities at the origin. On the thermodynamic side, we will show how the new black holes admit a maximum temperature, followed by the ``SCRAM phase'', a thermodynamic stable shut down, characterized by a positive black hole heat capacity.

How sure are you that spacetime is continuous? One approach to quantum gravity, causal set theory, models spacetime as a discrete structure: a causal set. This talk begins with a brief introduction to causal sets, then describes a new approach to modelling a quantum scalar field on a causal set. We obtain the Feynman propagator for the field by a novel procedure starting with the Pauli-Jordan commutation function. The candidate Feynman propagator is shown to agree with the continuum result. This model opens the door to physical predictions for scalar matter on a causal set.

The idea behind an intersection between loop quantum gravity and noncommutative geometry is to combine elements of unification with a setup of canonical quantum gravity. In my talk I will first review the construction of a semi-finite spectral triple build over an algebra of holonomy loops. Here, the loop algebra is a noncommutative algebra of functions over a configurations space of connections, and the interaction between the Dirac type operator and the loop algebra captures information of the kinematical part of canonical quantum gravity.