This series consists of talks in the area of Quantum Gravity.
We describe of the evaporation
process as driven by the dynamical evolution of the quantum gravitational
degrees of freedom resident at the horizon, as identified by the Loop Quantum
Gravity kinematics. Using a parallel with the Brownian motion, we interpret the
first law of quantum dynamical horizon in terms of a fluctuation-dissipation
relation applied to this fundamental discrete structure. In this way, the
horizon evolution is described in terms of relaxation to an equilibrium state
It is known that the entanglement entropy of quantum
fields on the black hole
background contributes to the Bekenstein-Hawking entropy,and that its
divergences can be absorbed into the renormalization of gravitational
couplings. By introducing a Wilsonian cutoff scale and the concepts of
the renormalization group, we can expand this observation
into a broader framework for understanding black hole entropy. At a
given RG scale, two contributions to the black hole entropy can be
combinatorial problems associated with the counting of black hole states in
loop quantum gravity can be analyzed by using suitable generating functions.
These not only provide very useful tools for exact computations, but can also
be used to perform an statistical analysis of the black hole degeneracy
spectrum, study the interesting substructure found in the entropy of
microscopic black holes and its asymptotic behavior for large horizon areas.
There are several
fundamental predictions of quantum field theory, such as Hawking radiation (i.e., black hole evaporation) or the Sauter-Schwinger effect (i.e., electron-positron pair creation out of the quantum vacuum by a strong electric field), which have so far eluded direct experimental verification.
However, it should be possible to gain some experimental access to these effects via suitable condensed matter analogues. In this talk, some possibilities for reproducing such fundamental
The space of convex polyhedra can be given a dynamical structure. Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space, which is in excellent agreement with loop gravity. Here we present investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. This results
In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation £ of possible causation: for p, q Î C, p £ q means that q is in p’s future light cone. Fotini Markopoulou has proposed that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, in essence, by the topos Set C of presheaves on Cop.
Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a conventional perturbation analysis.
We propose a new method of unifying gravity and the Yang-Mills fields by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a constrained Spin(4) ~SO(4) Plebanski action.
I will review the construction of lattice theories which maintain one or more exact supersymmetries for non zero lattice spacing concentrating in particular on the case of N=4 super Yang-Mills. Such lattice theories may be studied using Monte Carlo techniques borrowed from lattice QCD and can be used to explore issues in holography. In three dimensions the same constructions can be used to formulate a topological theory of gravity which we argue is equivalent to Witten's Chern Simons theory.
We introduce an exactly solvable model to test various proposals for the imposition of the spin foam simplicity constraints. This model is a three-dimensional Holst-Plebanski action for the gauge group SO(4), in which the simplicity constraints mimic the situation of the four-dimensional theory. In particular, the canonical analysis reveals the presence of secondary second class constraints conjugated to the primary ones.