KLEIN: a MATHEMATICA Package for Radar Polarimetry Based on Spinor and Tensor Algebra

Bebbington, D.H.O.; Göbel, Manfred

doi:10.1006/jsco.2000.0460

Cited by 2 publications

(3 citation statements)

References 7 publications

(8 reference statements)

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“…As for X AB ′ in (37), the singularity of the matrix (42), allow us to express it as the Kronecker product…”

Section: Spinors and Geometrymentioning

confidence: 99%

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Geometric Polarimetry—Part I: Spinors and Wave States

Bebbington

Carrea

2014

IEEE Trans. Geosci. Remote Sensing

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A new formal approach for the representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalized complex-analytic coherent wave as a generating line in the sphere of wave directions and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincaré sphere is now located in physical space, simply a coordination of the wave sphere, with its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor that we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.Index Terms-Bivectors, covariant and contravariant spinors and tensors, geometry, phase flag, Poincaré sphere, state of polarization.

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“…As for X AB ′ in (37), the singularity of the matrix (42), allow us to express it as the Kronecker product…”

Section: Spinors and Geometrymentioning

confidence: 99%

“…A MATHEMATICA package [42] has been developed in order to perform symbolic calculation with spinors and tensors for radar polarimetry using the Penrose-Rindler notation [33].…”

Section: B Conjugate Spacesmentioning

confidence: 99%

Geometric Polarimetry—Part I: Spinors and Wave States

Bebbington

Carrea

2014

IEEE Trans. Geosci. Remote Sensing

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“…Moreover I note that searches for tensor software on the internet will find, in addition to the sorts of package described here, packages or libraries aimed at numerical simulations in, for example, non-relativistic fluid dynamics or elasticity, which are disciplines making heavy use of tensors in flat space, often in curvilinear coordinates. (Conversely, CA systems which handle curved spaces can be used for calculations in such disciplines: see for example Bebbington and Göbel 2001 and Sect. 7.4 .)…”

Section: Introductionmentioning

confidence: 99%

Computer algebra in gravity research

MacCallum

2018

Living Rev Relativ

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The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR’s requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors; and applications of CA in GR are outlined.

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KLEIN: a MATHEMATICA Package for Radar Polarimetry Based on Spinor and Tensor Algebra

Abstract: This paper introduces and describes Klein, a Mathematica package, designed to be used as a support and verification tool for scientific calculations in radar polarimetry based on spinor and tensor algebra.

Cited by 2 publications

References 7 publications

Geometric Polarimetry—Part I: Spinors and Wave States

Geometric Polarimetry—Part I: Spinors and Wave States

Computer algebra in gravity research

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