Related papers: Lectures on the functional renormalization group m…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
We review the renormalization group method applied to non-equilibrium dynamics by tracing the way how the hydrodynamic equations can be derived as reduced dynamics of the Boltzmann equation as a typical example.
We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of…
These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
This manuscript aims at giving our new advance on the functional renormalization group applied to tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert…
We present an analytical method, rooted in the non-perturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the…
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…
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…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
Renormalization Group Equations in integro-differential form describing the evolution of cascades or resumming logarithmic scaling violations have been known in quantum field theory for a long time. These equations have been traditionally…
We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with…
We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural"…