Related papers: Optical theorem and unitarity
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…
Quantum attributes of light have been related to non-classicality so far, i. e. to incompatibility with mixtures of coherent states. The progress in quantum optics indicates that this feature does not suffice to witness exotic behavior of…
The enormous energy demand of artificial intelligence is driving the development of alternative hardware for deep learning. Physical neural networks try to exploit physical systems to perform machine learning more efficiently. In…
In this work, we study the analytic properties of S-matrix for unstable particles, which is defined as the residues on the unphysical sheets where unstable poles reside. We demonstrate that anomalous thresholds associated with UV physics…
Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…
The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some properties like the "uniqueness of orientation".
We analyze the unitarity of a non-relativistic non-commutative scalar field theory. We show that electric backgrounds spoil unitarity while magnetic ones do not. Furthermore, unlike its relativistic counterparts, unitarity can not be…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
The optical theorem is an important tool for scattering analysis in acoustics, electromagnetism, and quantum mechanics. We derive an extended version of the optical theorem for the scattering of elastic waves by a spherical inclusion…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a…
The restoration of an additive function defined on P parallelepipeds via its derivative with respect to P parallelepipeds is studied. The obtained theorem is applied to the questions of uniqueness of multiple series with regard to Haar and…