Related papers: Flow Equations for N Point Functions and Bound Sta…
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…
Using a continuous unitary transformation recently proposed by Wegner \cite{Wegner} together with an approximation that neglects irrelevant contributions, we obtain flow equations for Hamiltonians. These flow equations yield a diagonal or…
The flow equations of the renormalization group allow to analyse the perturbative $n$-point functions of renormalizable quantum filed theories. Rigorous bounds implying renormalizability permit to control large momentum behaviour, infrared…
We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general,…
We construct exact solutions to the functional renormalisation group equation of the O(N) model and the Gross-Neveu model at large N for $2<d<4$, without specifying the form of the regulator. This allows to investigate which quantities are…
It is shown in the framework of the N-component scalar model that the saddle point structure may generate non-trivial renormalization group flow. The spinodal phase separation can be described in this manner and a flat action is found as an…
The goal of this thesis is the development and implementation of a non-perturbative solution method for Wegner's flow equations. We show that a parameterization of the flowing Hamiltonian in terms of a scalar function allows the flow…
Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory's renormalization group flow. In this work, we use the functional renormalization group equation for the…
Wilson's exact renormalization group equations are derived and integrated for the relevant part of the pure Yang-Mills action. We discuss in detail how modified Slavnov-Taylor identities controle the breaking of BRST invariance in the…
We present a method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with…
We investigate the renormalization group flows of multicomponent scalar theories with $U(1)$ gauge symmetry using the functional renormalization group method. The scalar sector is built up from traces of matrix fields that belong to simple,…
We revisit the two-dimensional quantum Ising model by computing renormalization group flows close to its quantum critical point. The low but finite temperature regime in the vicinity of the quantum critical point is squashed between two…
Renormalization schemes and cutoff schemes allow for the introduction of various distinct renormalization scales for distinct couplings. We consider the coupled renormalization group flow of several marginal couplings which depend on just…
Renormalisation group approaches are tailor made for resolving the scale-dependence of quantum and statistical systems, and hence their phase structure and critical physics. Usually this advantage comes at the price of having to truncate…
We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional…
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the…
The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation…
We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the…
We study the exact renormalisation group flow for ultracold Fermi-gases in unitary regime. We introduce a pairing field to describe the formation of the Cooper pairs, and take a simple ansatz for the effective action. Set of approximate…
Within the framework of exact renormalization group flow equations, a scale-dependent transformation of the field variables provides for a continuous translation of UV to IR degrees of freedom. Using the gauged NJL model as an example, this…