Related papers: Renormalization Group Approach to Generalized Cosm…
By adding a linear term to a renormalization-group equation in a system exhibiting infinite-order phase transitions, asymptotic behavior of running coupling constants is derived in an algebraic manner. A benefit of this method is presented…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…
In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This…
I show that an application of renormalization group arguments may lead to significant corrections to the vacuum decay rate for phase transitions in flat and curved space-time. It can also give some information regarding its dependence on…
Several problems in physics, in particular the averaging problem in gravity, can be described in a formalism derived from the real-space Renormalization Group (RG) methods. It is shown that the RG flow is provided by the Ricci-Hamilton…
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…
The use of techniques from loop quantum gravity for cosmological models may solve some difficult problems in quantum cosmology. The solutions under a number of circumstances have been well studied. We will analyse the behaviour of solutions…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…
Phase-space descriptions are used to find qualitative features of the solutions of generalized scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. Previous results are summarized and new ones are presented…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
We review and extend in several directions recent results on the asymptotic safety approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
In this paper, we describe the first steps towards fully non-perturbative cosmology. We explain why the conventional methods used by cosmologists based on the ADM formulation are generally inadequate for this purpose and why it is…
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…
In the Earth-related coordinate system, we reconstruct the standard model of cosmology based on the assumption of the cosmological principle and the perfect gas (or fluid). We exactly solve Einstein's field equation involved. The solution…
We study the effective theory of the conformal factor near its infrared stable fixed point.The renormalization group equations for the effective coupling constants are found and their solutions near the critical point are obtained,…