On conformal powers of the Dirac operator on spin manifolds

Matthias Fischmann

Archivum Mathematicum (2014)

  • Volume: 050, Issue: 4, page 237-253
  • ISSN: 0044-8753

Abstract

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The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the Dirac operator. Finally, we will present polynomial structures for the first examples of conformal powers in terms of first order differential operators acting on the spinor bundle.

How to cite

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Fischmann, Matthias. "On conformal powers of the Dirac operator on spin manifolds." Archivum Mathematicum 050.4 (2014): 237-253. <http://eudml.org/doc/262122>.

@article{Fischmann2014,
abstract = {The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the Dirac operator. Finally, we will present polynomial structures for the first examples of conformal powers in terms of first order differential operators acting on the spinor bundle.},
author = {Fischmann, Matthias},
journal = {Archivum Mathematicum},
keywords = {conformal and spin geometry; conformal powers of the Dirac operator; conformal covariance; tractor bundle; tractor D-operator; conformal and spin geometry; conformal powers of the Dirac operator; conformal covariance; tractor bundle; tractor D-operator},
language = {eng},
number = {4},
pages = {237-253},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On conformal powers of the Dirac operator on spin manifolds},
url = {http://eudml.org/doc/262122},
volume = {050},
year = {2014},
}

TY - JOUR
AU - Fischmann, Matthias
TI - On conformal powers of the Dirac operator on spin manifolds
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 4
SP - 237
EP - 253
AB - The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the Dirac operator. Finally, we will present polynomial structures for the first examples of conformal powers in terms of first order differential operators acting on the spinor bundle.
LA - eng
KW - conformal and spin geometry; conformal powers of the Dirac operator; conformal covariance; tractor bundle; tractor D-operator; conformal and spin geometry; conformal powers of the Dirac operator; conformal covariance; tractor bundle; tractor D-operator
UR - http://eudml.org/doc/262122
ER -

References

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