Search results for "Mathematical analysis"

New representation of two-loop propagator and vertex functions

1994

We present a new method of calculating scalar propagator and vertex functions in the two-loop approximation, for arbitrary masses of particles. It is based on a double integral representation, suitable for numerical evaluation. Real and imaginary parts of the diagrams are calculated separately, so that there is no need to use complex arithmetics in the numerical program.

WITHDRAWN: Linear Response Theory with finite-range interactions

2021

Model-independent separation of structure functions over an extended kinematical region

1994

A method for the separation of structure functions in (e, e′ p) experiments is proposed, which is an extension of the traditional Rosenbluth-type techniques of [1,2]. In our approach, we use a very flexible Ansatz to describe the structure functions within an extended kinematical regionG and determine its free parameters with a x2 minimization. The procedure is tested by pseudo data (12C(e, e′p)11Bg.s.) in the quasi-free region.

Sweeping the Space of Admissible Quark Mass Matrices

2002

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to cover the general case, and of the polar decomposition theorem that allows to convert arbitrary nonsingular matrices to triangular form, we achieve a parameterization where the remaining freedom is reduced to one complex parameter. While this parameter runs through the domain bounded by a circle with radius R determined by the up-quark masses around the origin in the complex plane one sweeps the space of all mass matrices compatible with the given set of d…

A new technique for computing the spectral density of sunset-type diagrams: integral transformation in configuration space

1998

We present a new method to investigate a class of diagrams which generalizes the sunset topology to any number of massive internal lines. Our attention is focused on the computation of the spectral density of these diagrams which is related to many-body phase space in $D$ dimensional space-time. The spectral density is determined by the inverse $K$-transform of the product of propagators in configuration space. The inverse $K$-transform reduces to the inverse Laplace transform in any odd number of space-time dimensions for which we present an explicit analytical result.

Analytical solution for the solid angle subtended at any point by an ellipse via a point source radiation vector potential

2010

An axially symmetric radiation vector potential is derived for a spherically symmetric point source. This vector potential is used to derive a line integral for the solid angle subtended at a point source by a detector of arbitrary shape and location. An equivalent line integral given previously by Asvestas for optical applications is derived using this formulation. The line integral can be evaluated in closed form for important cases, and the analytical solution for the solid angle subtended by an ellipse at a general point is presented. The solution for the ellipse was obtained by considering sections of a right elliptic cone. The general solution for the ellipse requires the solution of …

Positioning in a flat two-dimensional space-time: the delay master equation

2010

The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one …

Fixed versus random triangulations in 2D Regge calculus

1997

Abstract We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the dl l measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random triangulations, which are obtained according to the standard Voronoi-Delaunay procedure. We compare both approaches quantitatively and show that the difference in the expectation value of R2 between the fixed and the random triangulation depends on the lattice size and the surface area A. We also try again to measure the string susceptibility exponents through a finite-size scaling Ansatz in the expectation value of an added R2 interaction term in an a…

Calculations for a disk source and a general detector using a radiation vector potential

2008

A closed form expression for a radiation vector potential is derived for a generalized disk radiation source. By applying Stokes's theorem the surface integral for the radiation flux into a general detector is converted into a much simpler line integral of the vector potential around the edge of the detector. This line integral can be easily evaluated for general detector geometry and general location and angular orientation relative to the disk source. For a number of cases the line integral reduces to integrals of Bessel functions which give various generalizations of Ruby's formula. Explicit formulas and numerical results for the geometric efficiency are given for circular and elliptical…

Introducing the Pietarinen expansion method into the single-channel pole extraction problem

2013

We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the nonsingular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the nonsingular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by …