Related papers: Introduction to Renormalisation
The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a…
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…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
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…
A fundamental length is introduced into physics in a way which respects the principles of relativity and quantum field theory. This improves the properties of quantum field theory: divergences are removed. How to quantize gravity is also…
Based only on simple principles of renormalization in coordinate space, we derive closed renormalized amplitudes and renormalization group constants at 1- and 2-loop orders for scalar field theories in general backgrounds. This is achieved…
This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A…
Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only…
Leading logarithms (LLs) in massless non-renormalizable effective field theories (EFTs) can be computed with the help of non-linear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity,…
Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…
The goal of this lecture is to introduce the student to the theory of Special Relativity. Not to overload the content with mathematics, the author will stick to the simplest cases; in particular only reference frames using Cartesian…
Lecture notes of a block course explaining why quantum field theory might be in a better mathematical state than one gets the impression from the typical introduction to the topic. It is explained how to make sense of a perturbative…
Using the spectral properties of orthogonal polynomials, we introduce a finite version of quantum field theory for elementary particles. Closed-loop integrals in the Feynman diagrams for computing transition amplitudes are finite.…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
Renormalization group methods are applied to a scalar field within a finite, nonlocal quantum field theory formulated perturbatively in Euclidean momentum space. It is demonstrated that the triviality problem in scalar field theory, the…
The purpose of this Chapter is to give a general introduction and status review on the perturbative approach to quantum gravity (QG). This text is a modified version of the corresponding chapters of Part II of the recent textbook on quantum…
In this talk I will present some of the main difficulties we encounter in studying the large scale behavior of disordered systems. This presentation will be done using a field theory language. The difficulties in applying the standard…
These notes provide an explanation of the type classification of von Neumann algebras, which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…