# Conformally covariant differential operators acting on spinor bundles and related conformal covariants

@inproceedings{Fischmann2013ConformallyCD, title={Conformally covariant differential operators acting on spinor bundles and related conformal covariants}, author={M. Fischmann}, year={2013} }

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 spin manifolds using the tractor machinery. We will also present a new family of conformally covariant linear differential operators on the standard spin tractor bundle. Furthermore, we generalize the existence proof of conformal power of the Dirac operator on Riemannian spin manifolds [GMP12] to semi… Expand

#### 6 Citations

On conformal powers of the Dirac operator on spin manifolds

- Mathematics
- 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… Expand

Conformal superalgebras via tractor calculus

- Mathematics, Physics
- 2015

We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of… Expand

The zero set of a twistor spinor in any metric signature

- Mathematics
- 2015

Using tractor methods, we exhibit the local structure of the zero set of a twistor spinor in any metric signature. It is given as the image under the exponential map of a distinguished totally… Expand

The Boundary Value Problem for Laplacian on Differential Forms and Conformal Einstein Infinity

- 2017

We completely resolve the boundary value problem for differential forms for conformal Einstein infinity in terms of the dual Hahn polynomials. Consequently, we present explicit formulas for the… Expand

Conformally Invariant Spinorial Equations in Six Dimensions

- Physics, Mathematics
- 2016

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out.… Expand

On conformal powers of the Dirac operator on Einstein manifolds

- Mathematics, Physics
- 2014

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 of… Expand

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