Scientific Series

We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. An \'effective gravitational field\' dominates the kinematics of small perturbations in an Analogue Model. In these models there is no obvious connection between the \'gravitational\' field tensor and the Einstein equations, as the emergent spacetime geometry arises as a consequence of linearising around some classical field. After a brief introduction on this topic, we present our recent contributions to the field.

We analyze how quantum complexity poses bounds to the simulation of quantum systems. While methods as Density Functional Theory (DFT) and the Density Matrix Renormalization Group (DMRG) work very well in practice, essentially nothing on the formal requirements is known. In this talk, we consider these methods from a quantum complexity perspective: First, we discuss DFT which encapsulates the difficulty of solving the Schroedinger equation in a universal functional and show that this functional cannot be efficiently computed unless several complexity classes collapse. Second, we consider DMRG, a method to deal with quantum spin chains, and show that even under reasonable assumptions -- a polynomial gap and matrix product ground states -- finding the ground state is still a computationally hard problem. Beyond pinpointing the limitations of the methods, this helps us to understand under which assumptions we might be able to prove their convergence.

We review how renormalization, born in quantum field theory has evolved into a rather universal tool to analyze the change of physical laws under scaling. Recent developments in non commutative geometry with hopefully potential applications to the quantization of gravity will be discussed.

The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value --- not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates. In this talk, I describe a simple reconstruction of the finite- dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, the importance of global gauge invariance, and the importance (or lack thereof) of assumptions concerning separated systems.

The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/antiquarks, for all values of coupling. The simplest example of quark/antiquark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressable as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and damped by increasing momentum transfer, while displaying physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. These results are compatible with an earlier, instanton, field-strength analysis of Reinhardt, et.al.

The Cosmic Microwave Background Radiation is our most important source of information about the early universe. Many of its features are in good agreement with the predictions of the so-called standard model of cosmology -- the Lambda Cold Dark Matter Inflationary Big Bang. However, the large-angle correlations in the microwave background exhibit several statistically significant anomalies compared to the predictions of the standard model. On the one hand, the lowest multipoles seem to be correlated not just with each other but with the geometry of the solar system. On the other hand, when we look at the part of the sky that we most trust -- the part outside the galactic plane, there is a dramatic lack of large angle correlations. So much so that no choice of angular powerspectrum can explain it if the alms are Gaussian random statistically isotropic variables of zero mean.

After reviewing Wilson\'s picture of renormalization, and the associated Exact Renormalization Group, I will show that no (physically acceptable) non-trivial fixed points exist for scalar field theory in D>=4. Consequently, an asymptotic safety scenario is ruled out, and the triviality of the theory is confirmed.

The boundary object is an ethnographic term that describes objects, processes, or words that cross between cultures or disciplines. Boundary objects are often the currency and the result of cross disciplinary practices. All manner of things, from software, to maps, to theories can provide a rich terrain for misunderstanding, tentative agreements or new insights. Case studies of cross-disciplinary art and science collaborations or design and engineering projects will provide examples.