This series consists of talks in the area of Quantum Gravity.
I describe how, within the group field theory (GFT) formalism for quantum gravity, we can:
1) provide a candidate description of the quantum building blocks of spacetime, bringing together ideas and mathematical structures from other quantum gravity formalisms;
2) apply powerful tools from quantum field theory, like the (perturbative and non-perturbative) renormalization group, to establish the quantum consistency of given GFT models and to study their continuum limit and phase structure;
In this talk, I will address a major conceptual and technical concern of non-perturbative quantum gravity: the quantum superposition of causal structures of space-times. I will discuss a class of theories that can address the problem, their flaws, and their relation to general relativity.
Einstein's causality is one of the fundamental principles underlying modern physical theories. Whereas it is readily implemented in classical physics founded on Lorentzian geometry, its status in quantum theory has long been controversial. It is usually believed that the quantum nature of spacetime at small scales induces the breakdown of causality, although there is no empirical evidence that would support such a view.
Constraint free initial data can be given for vacuum general relativity on a pair of intersecting null hypersurfaces. Moreover, the Poisson algebra of a set of such free null initial data has been found,but it has an unfamiliar structure, making its quantization difficult. We note that this algebra is essentially a sum of an infinite number of copies of the Poisson algebras of cylindrically symmetric gravity. Using the fact that cylindrically symmetric gravity is integrable we find new free data with an algebra more amenable to quantization.
Abstract: Complex networks describe interacting systems ranging from the brain to the Internet. While so far the geometrical nature of complex networks has been mostly neglected, the novel field of network geometry is crucial for gaining a deeper theoretical understanding of the architecture of complexity. At the same time, network geometry is at the heart of quantum gravity, since many approaches to quantum gravity assume that space-time is discrete and network-like at the quantum level.
The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.
A formulation of a limit of a sequence of finite non-commutative spectral triples is presented. Examples of the commutative limits are the coadjoint orbits of semisimple Lie groups.
I will give a broad overview of this old subject which has come back to light recently in connection with the issue of black hole evaporation. It will be an informal, black board talk.
The possibility of observing quantum gravitational phenomena, viewed as remote until not long ago, is increasingly considered to be plausible. A potentially observable phenomenon is the decay of black holes via a quantum gravitational tunneling akin to standard nuclear decay. Loop quantum gravity can be used to compute the corresponding lifetime. This could be much shorter than the Hawking radiation time, rendering the effect astrophysically relevant.