Projective structure, \widetildeSL(3,\mathbb R) and the symplectic Dirac operator

2016/04/15 by Holíková, Marie, Křižka, Libor, Somberg, Petr
#53C30 #53D05 #81R25 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1604.04376

Abstract

Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is \widetildeSL(3,\mathbb R).

Related

• Higher symmetries of symplectic Dirac operator
• A projective Dirac operator on ℂPⁿ and extended SUSY
• Dirac-like Affine Fields in 3D
• Generalised Jordan map, symplectic transformations and Dirac's representation of the 3 + 2 de Sitter group
• Dirac field in AdS₂ and representations of \widetildeSL(2,ℝ)