Search results for "Complex conjugate"
showing 5 items of 5 documents
Unequal rapidity correlators in the dilute limit of the JIMWLK evolution
2019
We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution in the color glass condensate effective field theory. We discuss a diagrammatic interpretation of the long-range con elators. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a Balitsky-Fadin…
Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter
1992
A shift-and-scale-invariant elliptic coordinate-transformed phase-only filter in proposed. The filter is built in three steps: the complex conjugate of a basic-size target spectrum is calculated, its phase-only part is taken, and then the elliptic coordinate transformation is made. In the extreme case the scale ratio of recognizable objects equals 1:1.5, permitting good recognition of object sizes S within the range 0.83/= S/= 1.25. Discrimination abilities and relative Horner efficiencies of a few versions of the filter are calculated.
Shift and scale-invariant correlator using a radially stretched phase-only filter
1995
A radial stretching of the phase only filter depending on the energy angular distribution of the target spectrum is used to perform shift and scale invariant pattern recognition. The complex conjugate of a basic size target Fourier transform and the cumulative energy angular distribution are calculated. Then the radially stretched filter providing the same energy contribution to the correlation peak independent on the target size is prepared and used in a conventional correlator, with spherical-wave illumination. The maximum scale ratio of recognizable objects equals 1:1.5. Computer simulations and experimental results, showing the performance of the filter are presented.
Towards an understanding of discrete ambiguities in truncated partial wave analyses
2017
It is well known that the observables in a single-channel scattering problem remain invariant once the amplitude is multiplied by an overall energy- and angle-dependent phase. This invariance is called the continuum ambiguity and acts on the infinite partial wave set. It has also long been known that, in the case of a truncated partial wave set, another invariance exists, originating from the replacement of the roots of partial wave amplitudes with their complex conjugate values. This discrete ambiguity is also known as the Omelaenko-Gersten-type ambiguity. In this paper, we show that for scalar particles, discrete ambiguities are just a subset of continuum ambiguities with a specific phase…
Unequal rapidity correlators in the dilute limit of JIMWLK
2019
We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution in the Color Glass Condensate effective field theory. We discuss a diagrammatic interpretation of the long-range correlators. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a BFKL picture i…