Twinor Theory: Field Equations from (A)dS4ℂ Spin-Tractors: A Twin to Twistor Theory Modelled on (A)dS4ℂ
Abstract
Twinor theory is formulated as a spacetime-based counterpart to twistor theory using holomorphic reductive Cartan geometry modelled on complexified (A)dS4. The fundamental spin-tractor bundle defines Dirac twinors, its symmetric powers define ladder twinors, and their extremal Lorentz components define chiral twinors. The general \textit{twinor field equation} is DY=J. Its adjacent contractions and mixed divergence are constrained by source relations; no additional equation is imposed on its completely symmetric projection. On a flat torsion-free Lorentzian background, the adjacent equations with the mass-normalization source and vanishing additional contracted sources, together with vanishing mixed divergence, reproduce the massive \textit{Dirac--Fierz--Pauli system}; the massless chiral realization gives the zero-rest-mass equations. Within the fixed mass normalization, the reality condition yielding a positive real mass squared is the \textit{anti-de Sitter reality condition} on the particle scale, independently of the cosmological scale and background curvature. The mass-coupling phase is therefore present in the classical connection before quantization. Nonlinear gravity is formulated through the full adjoint curvature, with energy--momentum and spin currents specifying Einstein--Cartan dynamics without requiring an action. The adjoint Bianchi identity constrains source compatibility, while a BGG-type sequence organizes torsion-free infinitesimal deformations. Matter interactions enter through the coupled connection and contracted source relations, with curvature compatibility recorded by DJ=ℱDY. Both chiralities are retained, and the additional consistency requirements for interacting higher-spin fields are distinguished from the underlying bundle construction.
Related
BibTeX
@misc{chien2026twinor,
title = {{Twinor Theory: Field Equations from $(A)dS_4^\mathbb C$ Spin-Tractors: A Twin to Twistor Theory Modelled on $(A)dS_4^\mathbb C$}},
author = {Chen-Hsu Chien},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40435},
eprint = {2610.40435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40435},
}
RIS
TY - UNPB
TI - Twinor Theory: Field Equations from (A)dS_4^ℂ Spin-Tractors: A Twin to Twistor Theory Modelled on (A)dS_4^ℂ
AU - Chen-Hsu Chien
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40435
UR - https://arxiv.org/abs/2610.40435
AB - Twinor theory is formulated as a spacetime-based counterpart to twistor theory using holomorphic reductive Cartan geometry modelled on complexified (A)dS_4. The fundamental spin-tractor bundle defines Dirac twinors, its symmetric powers define ladder twinors, and their extremal Lorentz components define chiral twinors. The general \textit{twinor field equation} is DY=J. Its adjacent contractions and mixed divergence are constrained by source relations; no additional equation is imposed on its completely symmetric projection. On a flat torsion-free Lorentzian background, the adjacent equations with the mass-normalization source and vanishing additional contracted sources, together with vanishing mixed divergence, reproduce the massive \textit{Dirac--Fierz--Pauli system}; the massless chiral realization gives the zero-rest-mass equations. Within the fixed mass normalization, the reality condition yielding a positive real mass squared is the \textit{anti-de Sitter reality condition} on the particle scale, independently of the cosmological scale and background curvature. The mass-coupling phase is therefore present in the classical connection before quantization. Nonlinear gravity is formulated through the full adjoint curvature, with energy--momentum and spin currents specifying Einstein--Cartan dynamics without requiring an action. The adjoint Bianchi identity constrains source compatibility, while a BGG-type sequence organizes torsion-free infinitesimal deformations. Matter interactions enter through the coupled connection and contracted source relations, with curvature compatibility recorded by DJ=ℱ_DY. Both chiralities are retained, and the additional consistency requirements for interacting higher-spin fields are distinguished from the underlying bundle construction.
ER -