相关论文: Renormalization Group Method and Reductive Perturb…
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…
Renormalization group equations are derived for the case when both valley splitting and intervalley scattering are present in a two-valley system. A third scaling parameter is shown to be relevant when the two bands are split but otherwise…
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…
Hierarchical renormalization group transformations are related to non-associative algebras. Non-trivial infrared fixed points are shown to be solutions of polynomial equations. At the example of a scalar model in $d(\ge2)$ dimensions some…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
When solving renormalisation group equations in a quantum field theory, one often specifies the boundary conditions at multiple renormalisation scales, such as the weak and grand-unified scales in a theory beyond the standard model. A point…
We discuss the formulation of "thermal renormalization group-equations" and their application to the finite temperature phase-transition of scalar O(N)-theories. Thermal renormalization group-equations allow for a computation of both the…
We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group…
In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one…
By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will…
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…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
Renormalization group methods are applied to a scalar field within a finite, nonlocal quantum field theory formulated perturbatively in Euclidean momentum space. It is demonstrated that the triviality problem in scalar field theory, the…
In this paper, we introduce a modified version of the renormalization group (RG) method and test its numerical accuracy. It has been tested on numerous scalar ODEs and systems of ODEs. Our method is primarily motivated by the possibility of…