1993/11/09 by William M. Pezzaglia, William Pezzaglia, Pezzaglia, William +3
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Algebraic and Geometric Analysis #Clifford algebra #Clifford analysis #Clifford bundle #Dirac algebra #Dirac equation #Dirac operator #FOS: Physical sciences #Gamma matrices #General Relativity and Quantum Cosmology (gr-qc) #Geometric algebra #Geometry #High Energy Physics - Theory (hep-th) #Mathematical physics #Mathematics #Multivector #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum and Classical Electrodynamics #Quantum mechanics #Scalar (mathematics) #Spinor #Vector bundle #Wave function #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.gr-qc/9311015
10 pages LaTex (kluwer.sty macro), report# clf-alg/pezz9304, [Summary of talk Sept. 22, 1993 at Ixtapa-Zihuatanejo, Mexico, XXIIth International Conference on Differential Geometric Methods in Theoretical Physics]
arxiv created 1993/11/09 · openalex publication_date 1993/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Multivector quantum mechanics utilizes wavefunctions which are Clifford aggregates (e.g. sum of scalar, vector, bivector). This is equivalent to multi- spinors constructed of Dirac matrices, with the representation independent form of the generators geometrically interpreted as the basis vectors of spacetime. Multiple generations of particles appear as left ideals of the algebra, coupled only by now-allowed right-side applied (dextral) operations. A generalized bilateral (two-sided operation) coupling is proposed which includes the above mentioned dextrad field, and the spin-gauge interaction as particular cases. This leads to a new principle of \it poly-dimensional covariance, in which physical laws are invariant under the reshuffling of coordinate geometry. Such a multigeometric superfield equation is proposed, which is sourced by a bilateral current. In order to express the superfield in representation and coordinate free form, we introduce Eddington E-F \it double-frame numbers. Symmetric tensors can now be represented as 4D ``dyads", which actually are elements of a global 8D Clifford algebra. As a restricted example, the dyadic field created by the Greider-Ross multivector current (of a Dirac electron) describes both electromagnetic and Morris- Greider gravitational interactions. [to appear in Proceedings edited by J. Keller, UNAM, Mexico (Kluwer Academic Publ)]