Related papers: Information Geometry and the Renormalization Group
The renormalization-group improved effective potential for an arbitrary renormalizable massless gauge theory in curved spacetime is found,thus generalizing Coleman-Weinberg's approach corresponding to flat space.Some explicit examples are…
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group…
Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and…
Based only on simple principles of renormalization in coordinate space, we derive closed renormalized amplitudes and renormalization group constants at 1- and 2-loop orders for scalar field theories in general backgrounds. This is achieved…
The asymptotic safety program builds on a high-energy completion of gravity based on the Reuter fixed point, a non-trivial fixed point of the gravitational renormalization group flow. At this fixed point the canonical mass-dimension of…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
We discuss the fundamental theoretical framework together with numerous results obtained by the authors and colleagues over an extended period of investigation on the Information Geometric Approach to Chaos (IGAC).
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
By using Renormalization Group methods we analyze the description of the Quantum Hall Fluid in terms of a dual plasma with dyons as effective degrees of freedom. The physical interpretation of the parameters of the model as the longitudinal…
We present a systematic study of one-loop quantum corrections in scalar effective field theories from a geometric viewpoint, emphasizing the role of field-space curvature and its renormalisation. By treating the scalar fields as coordinates…
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the…
Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
We develop a method to obtain the large N renormalization group flows for matrix models of 2 dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one matrix models. We show…
Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which…