Related papers: Teaching renormalization, scaling, and universalit…
We study quantum gravity in $2+\epsilon$ dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the…
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, weak spatial resolution, is investigated for a self…
We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible…
We study a simple class of unitary renormalization group transformations governed by a parameter f in the range [0,1]. For f=0, the transformation is one introduced by Wegner in condensed matter physics, and for f=1 it is a simpler…
The renormalization of the attractive 1/r^2 potential has recently been studied using a variety of regulators. In particular, it was shown that renormalization with a square well in position space allows multiple solutions for the depth of…
Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…
A hallmark of non-perturbative theories of quantum gravity is the absence of a fixed background geometry, and therefore the absence in a Planckian regime of any notion of length or scale that is defined a priori. This has potentially…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to…
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
The renormalization group flow in a general renormalizable gauge theory with a simple gauge group in 3+1 dimensions is analyzed. The flow of the ratios of the Yukawa couplings and the gauge coupling is described in terms of a bounded…
We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale…
In this work we attempt to show in a clear and simple manner the fundamental ideas of the Renormalization Theory. With that intention we use two well-known problems of the Physic and Engeneering undergraduate students, the calculation of…
We present a comprehensive discussion of the consistency of the effective quantum field theory of a single $Z_2$ symmetric scalar field. The theory is constructed from a bare Euclidean action which at a scale much greater than the…
Motivated by the conjecture that the cosmological constant problem is solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a class of…