Related papers: Introduction to Renormalisation
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the…
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…
This talk introduces perturbative quantum field on a heuristic level. It is directed at an audience familiar with elements of quantum mechanics, but not necessarily with high energy physics. It includes a discussion of the strategies behind…
Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive…
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are…
The normalization in the path integral approach to quantum field theory, in contrast with statistical field theory, can contain physical information. The main claim of this paper is that the inner product on the space of field…
We discuss how to implement an ``environmentally friendly'' renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for interpolating between the different effective…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
A definition is given, in the framework of stochastic quantization, for the dynamics of a system composed of classical and quantum degrees of freedom mutually interacting. It is found that the theory breaks reflection positivity, and hence…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
To unify the quantum electrodynamics (QED) under the first principle which brings the renormalization unartificially, we study Feynman diagrams in QED according to the set theory and the category theory. We add the restriction on the…
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to…
We give an introductory account to the renormalization of models without metric background. We sketch the application to certain discrete models of quantum gravity such as spin foam models.
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and…
This is a set of lecture notes for a graduate-level course on quantum algorithms, with an emphasis on quantum optimization algorithms. It is developed for applied mathematicians and engineers, and requires no previous background in quantum…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…