Related papers: A renormalization approach to irrational rotations
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is considered.
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…
We analyze by a renormalization method, the dynamics of a particle in a infinite square-well potential driven by an external monochromatic field. This method set up for Hamiltonian systems with two degrees of freedom allows us to analyze…
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit…
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a…
This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…
Various uses of the renormalization group are examined.
We use a renormalization group method, similar to that developed for random spin chains, to infer information about the layouts of cellular wireless networks.
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
This is a survey on renormalisation in the locality setup highlighting the role that locality morphisms can play for renormalisation purposes. Having set up a general framework to build regularisation maps, we illustrate renormalisation by…
We develop the exact renormalization group approach as a way to evaluate the effective speed of propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a…
This paper expands on existing learned models of human behavior via a measured step in structured irrationality. Specifically, by replacing the suboptimality constant $\beta$ in a Boltzmann rationality model with a function over states…
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.…
The "Krein" regularization method of quantum field theory is studied, inspired by the Krein space quantization and quantum metric fluctuations. It was previously considered in the one-loop approximation, and this paper is generalized to all…
We establish a novel type of connection between random walks and analytic number theory. Working with a random walk on the circle group $\mathbb{R}/\mathbb{Z}$ in which each step is a random integer multiple of a given quadratic irrational…
Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…