Related papers: Convolutions and Gaussians in Renormalization
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)],…
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…
The infinitesimal unitary transformation, introduced recently by F.Wegner, to bring the Hamiltonian to diagonal (or band diagonal) form, is applied to the Hamiltonian theory as an exact renormalization scheme. We consider QED on the light…
We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by…
We rigorously define renormalized evolution operator of the Schr\"odinger equation in the infinite dimensional Weyl-Moyal algebra for any time interval for arbitrary Hamiltonian depending on time. We state that for renormalizable field…
We propose an abstract framework describing energy-renormalized Hamiltonians in terms of local algebras. Within the framework, we examine the positivity improvingness of the semigroup generated by the renormalized Hamiltonian. As examples,…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
Schr\"odinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group…
A class of scalar models with non-polynomial interaction, which naturally admits an analytical resummation of the series of tadpole diagrams is studied in perturbation theory. In particular, we focus on a model containing only one…
In this talk I want to explain the operator substractions needed to renormalize gauge currents in a second quantized theory. The case of space-time dimensions $3+1$ is considered in detail. In presence of chiral fermions the renormalization…
The work of Kolmogorov, Arnold and Moser appeared just before the renormalization group approach to statistical mechanics was proposed by Wilson: it can be classified as a multiscale approach which also appeared in works on the convergence…
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.
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and…
We argue that the renormalizability of interacting quantum field theory on the curved-space background with an additional external antisymmetric tensor (two-form) field requires nonminimal interaction of the antisymmetric field with quantum…
We present a real-space renormalization group approach for the corner Hamiltonian, which is relevant to the reduced density matrix in the density matrix renormalization group. A set of self-consistent equations that the renormalized…
A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the…
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving…
We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…