This series consists of talks in the area of Quantum Gravity.
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)?
Combining the principles of general relativity and quantum theory still remains as elusive as ever. Recent work, that concentrated on one of the points of contact (and conflict) between quantum theory and general relativity, suggests a new perspective on gravity. It appears that the gravitational dynamics in a wide class of theories - including, but not limited to, standard Einstein's theory - can be given a purely thermodynamic interpretation. In this approach gravity appears as an emergent phenomenon, like e.g., gas or fluid dynamics.
Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which in turns reflects a non-trivial momentum-dependent statistics.
Loop quantum gravity and spin foams are two closely related theories of quantum gravity. There is an expectation that the sum over histories or path integral formulation of LQG will take the form of a spin foam, although a rigorous connection between the two is available only in 2+1 gravity. Understanding the relation between them will resolve many open questions of both theories. We probe the connection through an exactly soluble model of loop quantum cosmology. Beginning from the canonical theory we construct a spin foam like expansion of LQC.