Related papers: Regularisation as a quantised low-pass filter
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective…
The quantum kinetics of photons is studied directly in real time by implementing the dynamical renormalization group. In contrast to conventional approach, the dynamical renormalization group method consistently includes off-shell (energy…
Two approaches to nonperturbative renormalization are discussed for theories quantized on the light cone. One is tailored specifically to a calculation of the dressed-electron state in quantum electrodynamics, where an invariant-mass cutoff…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
The Kadanoff-Wilson-Fisher approach to renormalization is based upon studying the renormalization transform, which may be described as an action of the monoid $\mathbb{R}^{\times}_{\geq 1}$ on a suitable space of interactions. It is…
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…
We express the unitary time evolution in non-relativistic regularized quantum electrodynamics at zero and positive temperature by a Feynman integral defined in terms of a complex Brownian motion. An average over the quantum electromagnetic…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
In quantum field theory, elemental particles are assumed to be point particles. As a result, the loop integrals are divergent in many cases. Regularization and renormalization are necessary in order to get the physical finite results from…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries.…