Related papers: Information Geometry and the Renormalization Group
The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to providing a new interpretation of the density matrix renormalization group: its…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $\alpha$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic…
A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
Universal scaling laws only apply asymptotically near critical phase transitions. We propose a general scheme, based on normal form theory of renormalization group flows, for incorporating corrections to scaling that quantitatively describe…
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…
We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description,…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
Interactions growing slower than a certain exponential of the square of a scalar field, are well behaved when evolved under the functional renormalization group linearised around the Gaussian fixed point. They satisfy properties usually…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
The family $\mathcal{N}$ of $n$-variate normal distributions is parameterized by the cone of positive definite symmetric $n\times n$-matrices and the $n$-dimensional real vector space. Equipped with the Fisher information metric,…