On conformal powers of the Dirac operator on spin manifolds

@inproceedings{Fischmann2014OnCP,
  title={On conformal powers of the Dirac operator on spin manifolds},
  author={M. Fischmann},
  year={2014}
}
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… Expand
2 Citations
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References

SHOWING 1-10 OF 41 REFERENCES
On conformal powers of the Dirac operator on Einstein manifolds
We determine the structure of conformal powers of the Dirac operator on Einstein Spin-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques ofExpand
Conformally invariant powers of the ambient Dirac operator
This paper constructs a family of conformally invariant differential operators acting on spinor densities with leading part a power of the Dirac operator. The construction applies for all powers inExpand
Conformally invariant powers of the Dirac operator in Clifford analysis
The paper deals with conformally invariant higher-order operators acting on spinor-valued functions, such that their symbols are given by powers of the Dirac operator. A general classification resultExpand
Conformally covariant differential operators acting on spinor bundles and related conformal covariants
Conformal powers of the Dirac operator on semi Riemannian spin manifolds are investigated. We give a new proof of the existence of conformal odd powers of the Dirac operator on semi Riemannian spinExpand
Laplacian Operators and Q-curvature on Conformally Einstein Manifolds
A new definition of canonical conformal differential operators Pk (k = 1,2,...), with leading term a kth power of the Laplacian, is given for conformally Einstein manifolds of any signature. TheseExpand
Conformally invariant differential operators on Minkowski space and their curved analogues
This article describes the construction of a natural family of conformally invariant differential operators on a four-dimensional (pseudo-)Riemannian manifold. Included in this family are the usualExpand
Conformally invariant powers of the Laplacian — A complete nonexistence theorem
Conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo-Riemannian, Riemannian, conformai and related structures. This observationExpand
On conformally covariant powers of the Laplacian
We propose and discuss recursive formulas for conformally covariant powers $P_{2N}$ of the Laplacian (GJMS-operators). For locally conformally flat metrics, these describe the non-constant part ofExpand
Scattering matrix in conformal geometry
This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. TheExpand
A note on the conformal quasi-invariance of the Laplacian on a pseudo-Riemannian manifold
We consider the Laplacian on a pseudo-Riemannian manifold with constant scalar curvature (e.g. Euclidian space with an arbitrary signed inner product or its conformal compactification and coveringsExpand
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