Related papers: Convolutions and Gaussians in Renormalization
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a scalar field,…
We show within the Wilson renormalization group framework how the flow equation method can be used to prove the perturbative renormalizability of a relativistic massive selfinteracting scalar field. Furthermore we prove the regularity of…
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
An arbitrary form of complex potential perturbation in an oscillator consists of many exciting questions in open quantum systems. These often provide valuable insights in a realistic scenario when a quantum system interacts with external…
In close analogy to the Bloch-Feshbach formalism known from the theory of nuclear dynamics, I develop a mathematical framework that allows one to understand renormalization in terms of purely algebraic operations (projections, dilatations)…
Modified similarity renormalization of Hamiltonians is proposed, that performes by means of flow equations the similarity transformation of Hamiltonian in the particle number space. This enables to renormalize in the energy space the field…
A program to utilize the Tamm-Dancoff approximation, on the light-front, to solve relativistic quantum field theories, is presented. We present a well defined renormalization program for the Tamm-Dancoff approximation. This renormalization…
We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism…
Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the…
Using Wilsonian renormalization, we calculate the quantum correction to observable quantities, rather than the bare parameters, of the Higgs field. A physical parameter, such as a mass-squared or a quartic coupling, at an energy scale $\mu$…
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated…
The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…
We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally…
Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…
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…
An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS $s$-wave superconductor and a quantum spin. It is shown that known results…
We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the Density Matrix Renormalization Group, and makes use of the distribution of multipartite entanglement…
A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…
A general framework is presented for the renormalization of Hamiltonians via a similarity transformation. Divergences in the similarity flow equations may be handled with dimensional regularization in this approach, and the resulting…