This series consists of talks in the area of Quantum Gravity.
We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or
four-manifold as a branched cover. These data are expressed as
monodromies, in a way similar to the encoding of the gravitational field
via holonomies. We then describe convolution algebras of spin networks and
spin foams, based on the different ways in which the same topology can be
realized as a branched covering via covering moves, and on possible
The functional Renormalization Group is a continuum method to study quantum field theories in the non-perturbative regime. In Yang-Mills theory, it can be used to relate fully nonperturbative low-order correlation functions in particular gauges to observables such as confinement order parameters. As a special application, we determine the order of the phase transition and the critical temperature for various gauge groups (SU(N), N=3,.,12, Sp(2) and E(7)). This also allows to investigate what determines the order of the deconfinement phase transition.
Why is a vertical column of gas at thermal equilibrium slighly hotter at the bottom than a the top? My answer in this talk will be that time runs slower in a deeper gravitational potential, and temperature is nothing but the (inverse) speed of time. Specifically, I will (i) introduce Rovelli's notion of thermal time, (ii) use it to provide a "principle" characterization of thermal equilibrium in stationary spacetimes, and (iii) effortlessly derive the Tolman-Ehrenfest relation.
Interwiners describe quanta of space in loop quantum gravity. In this talk I show that the Hilbert space of SU(2) intertwiners has as semiclassical limit the phase space of a classical system originally considered by Minkowski: convex polyhedra with N facets of given areas and normals. This result sharpens Penrose spin-geometry theorem. The knowledge of the classical system associated to intertwiner space can be fruitfully used: I show that many properties of the spectrum of the volume operator can be derived via Bohr-Sommerfeld quantization of the volume of a classical polyhedron.
In the context of loop quantum gravity and spin foam models, the simplicity constraints are essential in that they allow to write general relativity as a constrained topological theory.
I will first recall the spin foam quantization procedure and focus more particularly on the step consisting in implementing the simplicity constraints.
An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. A scalar-tensor action describes classical gravity theory. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity. Also investigated are black holes and cosmology.
The Exact Renormalization Group (ERG) is a technique which can be fruitfully applied to systems with local interactions that exhibit a large number of degrees of freedom per correlation length. In the first part of the talk I will give a very general overview of the ERG, focussing on its applications in quantum field theory (QFT) and critical phenomena. In the second part I will discuss how a particular extension of the formalism suggests a new understanding of correlation functions in QFTs, in general, and gauge theories in particular.
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting models expanded about a suitable pseudofree theory [differing from a free theory by an $O(\hbar^2)$ term].
In my talk I would like to discuss the present status of Doubly Special Relativity. DSR is an extension of Special Relativity aimed at describing kinematics of particles and fields in the regime where (quantum) gravity effects might become relevant. I will discuss an interplay between DSR physics and mathematics of Hopf algebras.
A brief introduction to the notorious "cosmological constant problem" is given. Then, a particular approach is discussed, which has been developed by Volovik and the present speaker over the last years and which goes under the name of q-theory. This approach provides a possible solution of the main cosmological constant problem, why is |Lambda|^(1/4) negligible compared to the energy scales of the electroweak standard model (not to mention the Planck energy)?