2015/12/23 by G. Sardanashvily, Sardanashvily, G., A. Yarygin +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1512.07581
openalex publication_date 2015/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left multiplications, but not a group of its automorphisms. It is essential that such a Clifford algebra bundle contains spinor subbundles, and that it can be associated to a tangent bundle over a smooth manifold. This is just the case of gravitation theory. However, different these bundles need not be isomorphic. To characterize all of them, we follow the technique of composite bundles. In gravitation theory, this technique enables us to describe different types of spinor fields in the presence of general linear connections and under general covariant transformations.