2010
DOI: 10.1063/1.3541974
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Analytic extension of the K-matrix formalism

Abstract: Abstract. The importance is stressed of formulating a scattering theory that incorporates both unitarity in a multi-channel space and analyticity and in addition is consist with low energy theorems. Two very different possible approaches to come to such a model are presented, one based on solving an integral equation and one following a simpler algebraic approach. The latter is based on an extension of the K-matrix formalism into the complex momentum plane.

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Cited by 3 publications
(6 citation statements)
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“…Moreover, some positrons annihilate with electrons of air atoms producing further photons, and some photons ionize air atoms so that the electrons become part of the air shower. Thus, the electromagnetic cascade develops a negative net charge excess during the shower development of 20 − 30 % of the total number of electrons and positrons [40].…”
Section: Air Showersmentioning
confidence: 99%
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“…Moreover, some positrons annihilate with electrons of air atoms producing further photons, and some photons ionize air atoms so that the electrons become part of the air shower. Thus, the electromagnetic cascade develops a negative net charge excess during the shower development of 20 − 30 % of the total number of electrons and positrons [40].…”
Section: Air Showersmentioning
confidence: 99%
“…However, as explained in section 2.3, the shower front accumulates a negative net charge excess relevant for the radio emission and charge is totally conserved due to a positively charged plasma created behind the shower. Because of the high electron density at the shower axis the net charge excess is highest there and the excess of electrons can be as large as 20−30 % of the total number of electrons and positrons [40]. In a simplistic view the shower is a point charge whose strength changes during the shower development.…”
Section: Askaryan Effectmentioning
confidence: 99%
“…We will then make the assumption that this polarization is linear and oriented along v∧B. Not all geomagnetic induced fields have this property, but this is true in the geosynchrotron approach at small impact parameters [25] and in the transverse current approach [10]. Overall we will consider that the signal amplitude given by the EW dipole is proportional to |(v∧B) EW |, which is the magnitude of the vector cross product projected on the East-West axis (the orientation of the antennas).…”
Section: Physical Interpretationmentioning
confidence: 99%
“…This was supported by Allan using a different framework [7]. More recently, several comprehensive frameworks have been proposed [8,9,10]. The most advanced approach by Huege and collaborators [8] puts an emphasis on the geosynchrotron emission and gives a wealth of details on the associated radio emission pattern.…”
Section: Introductionmentioning
confidence: 99%
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