Related papers: Renormalization Group Functional Equations
Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the "exact" or "functional" renormalization group equation to derive the effective action $\Gamma_0$ by integrating…
We apply the functional renormalisation group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The…
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization…
Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art…
A renormalization group flow equation with a scale-dependent transformation of field variables gives a unified description of fundamental and composite degrees of freedom. In the context of the effective average action, we study the…
A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self--energy effects…
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a…
Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…
It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
We develop renormalization group methods for solving partial and stochastic differential equations on coarse meshes. Renormalization group transformations are used to calculate the precise effect of small scale dynamics on the dynamics at…
The renormalization group flow in two-dimensional field theories that are coupled to gravity has unusual features: First, the flow equations are second order in derivatives. Second, in the presence of handles the flow has quantum mechanical…
Two-loop renormalization group equations in gauge theories with multiple U(1) groups are presented. Instead of normalizing the abelian gauge fields in canonical forms, we retain kinetic-mixing terms and treat the mixing coefficients as free…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
By combining two distinct renormalization group transformations, opposing scale transformations, we obtain a composite transformation which does not rescale the system, and drives it to a "geometrical" fixed point, controlling the effective…
We review recent developments in functional renormalization group (RG) methods for interacting fermions. These approaches aim at obtaining an unbiased picture of competing Fermi liquid instabilities in the low-dimensional models like the…