相关论文: Coarse graining and renormalization

Definition of Feynman integrals as solutions of some well defined systems of differential equations is proposed. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that…

The standard (``fine-grained'') interpretation of quantum density functional theory, in which densities are specified with infinitely-fine spatial resolution, is mathematically unruly. Here, a coarse-grained version of DFT, featuring…

This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…

Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian. Observations using purely long distance…

The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams…

We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary…

The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microscopic spacetime physics to phenomenology at observationally…

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…

A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…

We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative…

We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative GFT (spin foam)…

It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue…

Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few "coarse"'…

Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…

The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…

We discuss a possible framework for the construction of a quantum gravity theory where the principles of QFT and general relativity can coexist harmonically. Moreover, in order to fix the correct gauge group of the theory we study the most…

We discuss the dependence of the coarse grained free energy and the classical interface tension on the coarse graining scale $k$. A stable range appears only if the renormalized dimensionless couplings at the critical temperature are small.…

I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…

We formulate the problem of finding the low-energy limit of spin foam models as a coarse-graining problem in the sense of statistical physics. This suggests that renormalization group methods may be used to find that limit. However, since…