相关论文: Bootstrapping Perturbative Perfect Actions
Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the…
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
The exact renormalisation group equation is studied for a two-dimensional theory with exponential interaction and a background charge at infinity. The motivation for studying this interaction is the flow between unitary minimal models…
We incorporate running parameters and anomalous dimensions into the framework of the exact renormalization group. We modify the exact renormalization group differential equations for a real scalar field theory, using the anomalous…
The renormalized trajectory of massless $\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
We compute the renormalized trajectory of $\phi^4_4$-theory by perturbation theory in a running coupling. We use an exact infinitesimal renormalization group. The expansion is put into a form which is manifestly independent of the scale…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions and compare the standard 2PI calculation with a modified version which uses a functional renormalization group method. The set of integral differential equations…
Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of…
We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length…
The general prescription for constructing the continuum limit of a field theory is explained using Wilson's renormalization group. We then formulate the renormalization group in perturbation theory and apply it to the four dimensional phi4…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
We study exact renormalization group equations in the framework of the effective average action. We present analytical approximate solutions for the scale dependence of the potential in a variety of models. These solutions display a rich…
In this paper, we give a rigorous proof of the renormalizability of the massive $\phi_4^4$ theory on a half-space, using the renormalization group flow equations. We find that five counter-terms are needed to make the theory finite, namely…
We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains…
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…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
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…
The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…