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A hallmark of non-perturbative theories of quantum gravity is the absence of a fixed background geometry, and therefore the absence in a Planckian regime of any notion of length or scale that is defined a priori. This has potentially…
The formulation of an exact functional renormalization group equation for Quantum Einstein Gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of…
In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…
We explore the properties of a recently proposed background independent exact renormalization group approach to gauge theories and gravity. In the process we also develop the machinery needed to study it rigorously. The proposal comes with…
We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a…
Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…
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…
The importance of the proper treatment of the wave function renormalization in the renormalization group analysis of quantum gravity is pointed out. The renormalization factor, sometimes called an inessential coupling, can be used to fix…
Motivated by the conjecture that the cosmological constant problem could be solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a…
The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution…
We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing…
General relativity (GR) extensions based on renormalization group (RG) flows may lead to scale-dependent couplings with nontrivial effects at large distance scales. Here we develop further the approach in which RG effects at large distance…
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 investigate the exact renormalization group (RG) in Einstein gravity coupled to N-component scalar field, working in the effective average action formalism and background field method. The truncated evolution equation is obtained for the…
The paper describes an explicit variational modification of the standard RSRG method and its application to quantum spin lattice systems. The modified approach is applied to exactly solvable ITF, XX and isotropic Heisenberg models. Better…
We briefly review the previous works on the renormalization group in quantum general relativity with the cosmological constant, based on the Vilkovisky and DeWitt version of effective action. On top of that, we discuss the prospects of the…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art…