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Abstract <p>A new approach to spinor field theory is developed on the basis of a non-trivial extension of the Lorentz spin group to a de Sitter group, which leads to a generalized Dirac equation. Within the framework of this model, it is shown that fundamental spin variables generate an induced geometric structure on the spacetime manifold. We clarify the importance of the Kerr–Schild representation in the new field-theoretical approach making it helpful for the study of the chirality issue and a possible violation of Lorentz symmetry.</p>

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Spin Geometry of Spacetime in the Dirac Theory

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Yuri N. Obukhov

摘要

Abstract

A new approach to spinor field theory is developed on the basis of a non-trivial extension of the Lorentz spin group to a de Sitter group, which leads to a generalized Dirac equation. Within the framework of this model, it is shown that fundamental spin variables generate an induced geometric structure on the spacetime manifold. We clarify the importance of the Kerr–Schild representation in the new field-theoretical approach making it helpful for the study of the chirality issue and a possible violation of Lorentz symmetry.