Related papers: Wave Function Renormalization for Particle-Field I…
We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A discussion of the structure of the renormalization group equation for a general Hamiltonian system is also given.
We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete…
It is shown how to construct renormalization group flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization…
The problem considered here is the determination of the hamiltonian of a first quantized nonrelativistic particle by the help of some measurements of the location with a finite resolution. The resulting hamiltonian depends on the resolution…
We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…
We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction…
We show a Wolfram model whose renormalization generates a sequence of approximations of a wave function having the Pauli-x matrix as Hamiltonian.
Ultraviolet (UV) renormalization of the Nelson model in quantum field theory is considered. A relationship between a ultraviolet renormalization term and the ground state energy of the Hamiltonian with total momentum zero is studied by…
We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that successively decouples the high-frequency…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective…
We consider a translation-invariant Pauli-Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We…
A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian…
Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the zero cutoff limit a self-adjoint operator exists after a logarithmically divergent term…
We illustrate the mass and charge renormalization procedures in quantum field theory using, as an example, a simple model of interacting electrons and photons. It is shown how addition of infinite renormalization counterterms to the…
In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form…
Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to…
The purpose of these notes is to provide a pedagogical introduction to the concept of renormalization in atomic physics. We study quantum dynamics of a model of a nonrelativistic single electron atom coupled to the quantum radiation field…