Related papers: Renormalization group methods and the 2PI effectiv…
The Polchinski version of the exact renormalization group equation is discussed and its applications in scalar and fermionic theories are reviewed. Relation between this approach and the standard renormalization group is studied, in…
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 show that the so-called Phi-derivable approximations can be combined with the exact renormalization group to provide efficient non-perturbative approximation schemes. On the one hand, the Phi-derivable approximations allow for a simple…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
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…
Renormalization group procedure for effective particles in the front form of Hamiltonian dynamics is applied to an elementary quantum field theory for two species of particles mixed through a mass-like interaction term. The model…
We discuss the renormalizability of Phi-derivable approximations in scalar phi^4 theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet…
We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply…
The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of…
We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phase.…
Approximations based on two-particle irreducible (2PI) effective actions (also known as $\Phi$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and…
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field…
Some recent all-loop results on the renormalization of supersymmetric theories are summarized and reviewed. In particular, we discuss how it is possible to construct expressions which do not receive quantum corrections in all orders for…
The Symmetry Improved Two-Particle-Irreducible (SI2PI) formalism is a powerful tool to calculate the effective potential beyond perturbation theory, whereby infinite sets of selective loop-graph topologies can be resummed in a systematic…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…
Resummations of infinite sets of higher-order perturbative contributions are often needed both in thermal field theory and at zero temperature. For instance, the behaviour of the Standard Model (SM) effective potential extrapolated to very…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…