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A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation…
We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…
In a wide class of potentials the exact asymptotic dependence on finite distance R from scattering center is established for outgoing differential flux. It is shown how this dependence is eliminated by integration over solid angle for total…
Power corrections in QCD (both conventional and unconventional ones arising from the ultraviolet region) are discussed within the infrared finite coupling-dispersive approach. It is shown how power corrections in Minkowskian quantities can…
The idea of reduction of couplings in renormalizable theories will be presented and then will be applied in Particle Physics models. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group…
The space of solutions of the exact renormalization group fixed point equations of the two-dimensional $RP^{N-1}$ model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of $N\geq…
In two and three dimensions, the standard treatment of the scattering problem for a multi-delta-function potential, $v(\mathbf{r})=\sum_{n=1}^N\mathfrak{z}_n\delta(\mathbf{r}-\mathbf{a}_n)$, leads to divergent terms. Regularization of these…
A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be…
In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…
We analyze quantitatively the interplay between explicit and implicit renormalization in Nuclear Physics. By explicit renormalization we mean to integrate out higher energy modes below a given cutoff scale using the similarity…
We explore the effects on nuclear bulk properties of using regularization cutoffs larger than the nucleon mass within the chiral effective field theory with a power counting that ensures order-by-order renormalization in the two-nucleon…
We discuss the subleading contact interactions, or counterterms, of the triplet channels of nucleon-nucleon scattering in the framework of chiral effective field theory, with S and P waves as the examples. The triplet channels are special…
We consider a new approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Starting with a Lorentz-invariant form of the effective Lagrangian we work out…
Due to an accidentally large $s$-wave scattering length, in a relatively wide range of energy, neutrons are approximately described by the nonrelativistic conformal field theory of unitarity fermions, perturbed by one relevant and an…
We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for $O(N)$-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder…
Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop…
We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…
We suggest a method of singular terms regularization in potential model of $N\bar{N}$ interaction. This method is free from any uncertainties, related to the usual cut-off procedure and based on the fact, that in the presence of…
We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length…
The observed IR and the spectator UV particles of a regulated, cutoff quantum field theory are entangled by their interactions; hence, the IR sector can be described by the help of the density matrix only. The tree-level renormalized…