Related papers: Mathematical renormalization in quantum electrodyn…
In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
We give an introductory account to the renormalization of models without metric background. We sketch the application to certain discrete models of quantum gravity such as spin foam models.
We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show…
These lectures illustrate the key ideas of modern renormalization theory and effective field theories in the context of simple nonrelativistic quantum mechanics and the Schr\"odinger equation. They also discuss problems in QED, QCD and…
We study a recently proposed quantum action depending on temperature. We construct a renormalisation group equation describing the flow of action parameters with temperature. At zero temperature the quantum action is obtained analytically…
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit…
This lecture provides an introduction to the renormalisation group as applied to scattering of two nonrelativistic particles. As well as forming a framework for constructing effective theories of few-nucleon systems, these ideas also…
Renormalization group procedure for effective particles in the front form of Hamiltonian dynamics is applied to an elementary quantum field theory for two species of particles mixed through a mass-like interaction term. The model…
The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive…
We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…
We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to…
This article presents a tutorial introduction to a recently developed real-time renormalization group method. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We illustrate the technique…
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic…
Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the approaches to study them is, firstly, to find formal solutions…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…