This series consists of talks in the area of Quantum Gravity.
Spin foam models aim at defining non-perturbative and background independent amplitudes for quantum gravity. In this work, I argue that the dynamics and the geometric properties of spin foam models can be nicely studied using recursion relations. In 3d gravity and in the 4d Ooguri model, the topological invariance leads to recursion relations for the amplitudes. I also derive recursions from the action of holonomy operators on spin network functionals.
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.
The relation between loop quantum gravity (LQG) and ordinary quantum field theory (QFT) on a fixed background spacetime still bears many obstacles. When looking at LQG and ordinary QFT from a mathematical perspective it turns out that the two frameworks are rather different: Although LQG is a true continuum theory its Hilbert space is defined in terms of certain embedded graphs which are labeled by irreducible representations of SU(2).
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.
We review some recent results on tachyon nonperturbative solutions of the nonlocal, lowest-level, effective action of string field theory. It is shown how nonlocality is encoded in a spacetime diffusion equation and how the latter emerges from the symmteries of the full, background-independent theory.
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.
Collisions and subsequent decays of higher dimensional branes leave
behind three-dimensional branes, one of which could play the role of
our universe. This process also leads to the production of
one-dimensional branes, D-strings, and fundamental ones (F-strings),
known as cosmic superstrings. In the first part of this talk, I will discuss the mechanism we have proposed in order to explain the origin of the space-time dimensionality, while in the second part I will review formation and dynamics of cosmic superstrings.
I will discuss the contribution to black hole thermodynamics from a variation in the cosmological constant. The description of black hole with a cosmological constant is facilitated by introducing a two-form potential for the static Killing field. The resulting Smarr formula then includes a term proportional to the cosmological constant times an effective volume, which arises as the difference between the Killing potential on the horizon and the boundary at infinity.
As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we analyze the physical consequences of including inhomogeneities. We consider a gravitational model in vacuo which possesses local degrees of freedom, namely, the linearly polarized Gowdy cosmologies. We carry out a hybrid quantization which combines loop and Fock techniques.