Conformally invariant powers of the ambient Dirac operator

Abstract

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 in odd dimensions, and only for finitely many powers in even dimensions. These operators arise naturally as obstructions to formal solution of the Dirac equation on the Fefferman-Graham ambient space with prescribed boundary conditions.

16 pages

References in corpus (2)

• Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus
• Scattering Matrix in Conformal Geometry

Cited by in corpus (7)

• On the Clifford-Fourier transform
• Conformal geometry of the supercotangent and spinor bundles
• Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras
• Conformally invariant operators, differential forms, cohomology and a generalisation of Q-curvature
• Almansi Theorems in Umbral Clifford Analysis and the Quantum Harmonic Oscillator
• The boundary value problem for Laplacian on differential forms and conformally Einstein infinity
• Residue Family Operators on Spinors and Spectral Theory of Dirac operator on Poincaré-Einstein Spaces