2025/12/20 by S. V. Rumyantseva, Rumyantseva, S. V., D. S. Shirokov +1
Mathematics · Physics and Astronomy · #15A66 #35Q41 #70S15 #81Q05 #81T13 #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics and Applications #Noncommutative and Quantum Gravity Theories
paper · doi:10.48550/arxiv.2512.18347
openalex publication_date 2025/12/20 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
This paper investigates the Lorentz invariance of the multidimensional Dirac-Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct approaches: the tensor formulation and the spinor formulation. We first present a detailed examination of the four-dimensional Dirac-Hestenes equation, comparing both transformation approaches. These results are subsequently generalized to the multidimensional case with (1,n) signature. The tensor approach requires explicit invariants, while the spinor formulation naturally maintains Lorentz covariance through spin group action.