Quantum Gravity

A serious shortcoming of spinfoam loop gravity is the absence of matter. I present a minimal and surprisingly simple coupling of a chiral fermion field in the framework of spinfoam quantum gravity. This result resonates with similar ones in early canonical loop theory: the naive fermion hamiltonian was found to be just the extension of the simple

Emergent gravity scenarios have become increasingly popular in recent times. In this talk I will review some evidence in this sense and discuss some lessons from toy models based on condensed matter analogues of gravity. These lessons suggest some (possibly) general features of the emergent gravity framework which not only can be tested with current astrophysical observations but can also improve our understanding of cosmological puzzles such as the dark energy one. I shall review these tests and expectations and discuss the perspectives of this line of research and emergent gravity scenarios at large.

Usually in quantum field theory one considers two different interpretations: 1: The field is an infinite number of quantum oscillators, giving rise to a wave functional \Psi(\phi). 2: The positive frequency component of a field, \phi_+(x), is a wave function analogous to standard quantum mechanics. While interpretation 2 is often only mentioned implicitly it is crucial to standard computations of measurable scattering probabilities. We extend the interpretation of QFT as relativistic quantum mechanics (option 2) and show how the total Klein Gordon field which consists of positive and negative frequency contributions, \phi = \phi_+ + \phi_- , can be interpreted as a wave function. Our construction manifestly shows that signal propagation in QFT cannot exceed the speed of light. This follows from the replacement of the Feynman propagator by the Wheeler propagator, which is just the time ordered commutator. Our second observation is that interpretation 2 is not consistent if one uses the Newton Wigner position operator, therefore we introduce a more natural bilinear position operator. We show by an explicit example that the bilinear operator, contrary to the Newton Wigner operator, allows relativistic particles to be perfectly localized, precisely as in non relativistic quantum mechanics.

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 composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry. (Based on joint work with Domenic Denicola and Ahmad Zainy al-Yasry)

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. Furthermore we study the non-perturbative effective potential for the field strength, where we observe the formation of a gluon condensate in the vacuum.

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. This approach contrasts with the "constructive" accounts of thermal equilibrium in curved spacetimes given in the literature, and vindicates the time-temperature relationship cropping up in the Hawking-Unruh and Kubo-Martin-Schwinger relations.

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. Then, I will present the U(N) framework initially developed for SU(2) intertwiners. Finally, I will show how we can apply this new framework to impose the simplicity constraints in the context of 4d Euclidean gravity and present new solutions defined in term of U(N) coherent states.

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]. This procedure not only provides acceptable solutions for models for which no acceptable solution currently exists, e.g., $\varphi^4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free solution, for less-singular models as well, e.g., $\varphi^4_n$, for $n=2,3$.

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.