Related papers: Practical Algebraic Renormalization
If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We…
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)…
These lecture notes give an introduction to the algebraic renormalization of the Standard Model. We start with the construction of the tree approximation and give the classical action and its defining symmetries in functional form. These…
Quantum neural networks (QNNs) provide expressive probabilistic models by leveraging quantum superposition and entanglement, yet their practical training remains challenging due to highly oscillatory loss landscapes and noise inherent to…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota-Baxter anti-homomorphism from general regularized functionals on…
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…
In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
We introduce an approach for calculating the quantum loop corrections in the $\phi^4$ theory. Differential regularization and background-field method are essential tools and are used to calculate the effective action of the theory to…
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions,…
We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses…
We show how to reliably calculate quantum gravitational corrections to cosmological models using the unique effective action formalism for quantum gravity. Our calculations are model independent and apply to any ultra-violet complete theory…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and…
In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=\lambda/\lambda$.…
The non-local regularization is a powerfull method to regularize theories with an action that can be decomposed in a kinetic and an interacting part. Recently it was shown how to regularize the Batalin-Vilkovisky field-antifield formalism…
Explicit analytic expressions for the electron self-energy and the vertex correction in quantum electrodynamics are derived at one loop using the recently proposed regularization scheme known as denominator regularization, assisted by its…
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need…