Algebraic analysis of the Rarita-Schwinger system in real dimension three

Alberto Damiano

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 197-211
  • ISSN: 0044-8753

Abstract

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In this paper we use the explicit description of the Spin– 3 2 Dirac operator in real dimension 3 appeared in (Homma, Y., The Higher Spin Dirac Operators on 3 –Dimensional Manifolds. Tokyo J. Math. 24 (2001), no. 2, 579–596.) to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita–Schwinger operators. We make use of the general theory provided by (Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac systems and computational algebra, Progress in Mathematical Physics, Vol. 39, Birkhäuser, Boston, 2004.) and some standard Gröbner Bases techniques. Our aim is to show that such operator shares many of the algebraic properties of the Dirac operator in real dimension four. In particular, we prove the exactness of the associated algebraic complex, a duality result and we explicitly describe the space of polynomial solutions.

How to cite

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Damiano, Alberto. "Algebraic analysis of the Rarita-Schwinger system in real dimension three." Archivum Mathematicum 042.5 (2006): 197-211. <http://eudml.org/doc/249773>.

@article{Damiano2006,
abstract = {In this paper we use the explicit description of the Spin–$\frac\{3\}\{2\}$ Dirac operator in real dimension $3$ appeared in (Homma, Y., The Higher Spin Dirac Operators on $3$–Dimensional Manifolds. Tokyo J. Math. 24 (2001), no. 2, 579–596.) to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita–Schwinger operators. We make use of the general theory provided by (Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac systems and computational algebra, Progress in Mathematical Physics, Vol. 39, Birkhäuser, Boston, 2004.) and some standard Gröbner Bases techniques. Our aim is to show that such operator shares many of the algebraic properties of the Dirac operator in real dimension four. In particular, we prove the exactness of the associated algebraic complex, a duality result and we explicitly describe the space of polynomial solutions.},
author = {Damiano, Alberto},
journal = {Archivum Mathematicum},
keywords = {Dirac operator; Gröbner basis; Rarita-Schwinger system; Cauchy-Fueter system},
language = {eng},
number = {5},
pages = {197-211},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Algebraic analysis of the Rarita-Schwinger system in real dimension three},
url = {http://eudml.org/doc/249773},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Damiano, Alberto
TI - Algebraic analysis of the Rarita-Schwinger system in real dimension three
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 197
EP - 211
AB - In this paper we use the explicit description of the Spin–$\frac{3}{2}$ Dirac operator in real dimension $3$ appeared in (Homma, Y., The Higher Spin Dirac Operators on $3$–Dimensional Manifolds. Tokyo J. Math. 24 (2001), no. 2, 579–596.) to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita–Schwinger operators. We make use of the general theory provided by (Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac systems and computational algebra, Progress in Mathematical Physics, Vol. 39, Birkhäuser, Boston, 2004.) and some standard Gröbner Bases techniques. Our aim is to show that such operator shares many of the algebraic properties of the Dirac operator in real dimension four. In particular, we prove the exactness of the associated algebraic complex, a duality result and we explicitly describe the space of polynomial solutions.
LA - eng
KW - Dirac operator; Gröbner basis; Rarita-Schwinger system; Cauchy-Fueter system
UR - http://eudml.org/doc/249773
ER -

References

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