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Functional renormalization group methods formulated in the real-time formalism are applied to the $O(N)$ symmetric quantum anharmonic oscillator, considered as a $0+1$ dimensional quantum field-theoric model, in the next-to-leading order of…
The large N_f self-consistency programme is reviewed. As an application the QCD beta-function is computed at O(1/N_f) and the anomalous dimensions of polarized twist-2 singlet operators are determined at the same order.
Perturbation theory and renormalization group methods are used to derive a finite-size scaling theory for the partition function zeroes and thermodynamic functions in the $O(n)$ $\phi^4$ model in four dimensions. The leading power--law…
To resum large logarithms in multi-scale problems a generalization of $\MS$ is introduced allowing for as many renormalization scales as there are generic scales in the problem. In the new \lq\lq minimal multi-scale subtraction scheme''…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
We review the development of the large $N$ method, where $N$ indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories. The relevant historical background is summarized as a…
We investigate the reliability of the large $N_f$ expansion of four-dimensional gauge-fermion quantum field theories, focusing on the structure and scheme dependence of the beta function. While the existence of a nontrivial UV fixed point…
We propose a method to solve the Non Perturbative Renormalization Group equations for the $n$-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the $n$-point…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
In this paper we shall study whether dissipation in a $\lambda\phi^{4}$ may be described, in the long wavelength, low frequency limit, with a simple Ohmic term $\kappa\dot{\phi}$, as it is usually done, for example, in studies of defect…
This is an expository account of Balaban's approach to the renormalization group. The method is illustrated with a treatment of the the ultraviolet problem for the scalar phi^4 model on toroidal lattice in dimension d=3. In this second…
Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in…
In an earlier publication, we have introduced a method to obtain, at large N, the effective action for d-dimensional manifolds in a N-dimensional disordered environment. This allowed to obtain the Functional Renormalization Group (FRG)…
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr\"odinger-invariant n-point…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
The critical $O(N)$ CFT in spacetime dimensions $2 < d < 4$ is one of the most important examples of a conformal field theory, with the Ising CFT at $N=1$, $2 \leq d < 4$, as a notable special case. Apart from numerous physical…