1994/02/01 by László B. Szabados, L. B. Szabados · 41 citations
Mathematics · Physics and Astronomy · #Algebraic number #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Differential geometry #Gauge theory #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Spin connection #Spinor #Torsion (gastropod) #Twistor space #Twistor theory #gr-qc
paper · pdf · doi:10.1088/0264-9381/11/7/019
published in Classical and Quantum Gravity 11(7), 1833-1846 (IOP Publishing) · 14 pages, Plain Tex, no report number
arxiv created 1994/02/01 · openalex publication_date 1994/07/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The two-dimensional version of the Sen connection for spinors and tensors on spacelike 2-surfaces is constructed. A complex metric on the spin spaces is found which characterizes both the algebraic and extrinsic geometrical properties of the 2-surface . The curvature of the two-dimensional Sen operator is the pullback to of the anti-self-dual part of the spacetime curvature, while its `torsion' is a boost-gauge invariant expression of the extrinsic curvatures of . The difference between the two-dimensional Sen and the induced spin connections is the anti-self-dual part of the `torsion'. The irreducible parts of are shown to be the familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten type identities are derived; the first is an identity between the two-dimensional twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's charge integral, while the second contains the `torsion' as well. For spinor fields satisfying the 2-surface twistor equation the first reduces to Tod's formula for the kinematical twistor.