Related papers: Asymptotic solutions in asymptotic safety
In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R>0. We…
This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This…
This thesis is devoted to exploring various fundamental issues within asymptotic safety. Firstly, we study the reconstruction problem and present two ways in which to solve it within the context of scalar field theory, by utilising a…
We study an $f(R)$ approximation to asymptotic safety, using a family of non-adaptive cutoffs, kept general to test for universality. Matching solutions on the four-dimensional sphere and hyperboloid, we prove properties of any such global…
We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure.…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
In this work we study a significantly enlarged truncation of conformally reduced quantum gravity in the context of Asymptotic Safety, including all operators that can be resolved in such a truncation including up to the sixth order in…
We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to…
Asymptotic safety is a remarkable example when fruitful ideas borrowed from statistical physics proliferate to high-energy physics. The concept of asymptotic safety is tightly connected to fixed points (FPs) of the renormalization-group…
We summarize the status of constructing fixed functionals within the f(R)-truncation of Quantum Einstein Gravity in three spacetime dimensions. Focusing on curvatures much larger than the IR-cutoff scale, it is shown that the fixed point…
Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
Finite dimensional truncations and the single field approximation have thus far played dominant roles in investigations of asymptotic safety for quantum gravity. This thesis is devoted to exploring asymptotic safety in infinite dimensional,…
Asymptotic safety generalizes asymptotic freedom and could contribute to understanding physics beyond the Standard Model. It is a candidate scenario to provide an ultraviolet extension for the effective quantum field theory of gravity…
A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this paper we provide general tools for checking if a function possesses this property. First we prove equivalence of…
This is an introduction to asymptotically safe quantum gravity, explaining the main idea of asymptotic safety and how it could solve the problem of predictivity in quantum gravity. In the first part, the concept of an asymptotically safe…
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
We study fixed points of quantum gravity with renormalisation group methods, and a procedure to remove convergence-limiting poles from the flow. The setup is tested within the $f(R)$ approximation for gravity by solving exact recursive…