Geometric tri-product of the spin domain and Clifford algebras
نویسنده
چکیده
We show that the triple product defined by the spin domain (Bounded Symmetric Domain of type 4 in Cartan’s classification) is closely related to the geometric product in Clifford algebras. We present the properties of this tri-product and compare it with the geometric product. The spin domain can be used to construct a model in which spin 1 and spin1/2 particles coexist. Using the geometric tri-product, we develop the geometry of this domain. We present a geometric spectral theorem for this domain and obtain both spin 1 and spin 1/2 representations of the Lorentz group on this domain. MSC : 15A66; 17C90 PACS : 02.10.De; 12.60.Jv.
منابع مشابه
Geometric (Clifford) algebra and its applications
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to define Clifford algebras with scalars in arbitrary rings and provides new suggestions for an infinite-dimensional approach. Furthermore, I give a quick review...
متن کاملDerivations on Certain Semigroup Algebras
In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.
متن کاملp-Analog of the Semigroup Fourier-Steiltjes Algebras
In this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.
متن کاملGrade free product formulæ from Graßmann Hopf gebras
In the traditional approaches to Clifford algebras, the Clifford product is evaluated by recursive application of the product of a one-vector (span of the generators) on homogeneous i.e. sums of decomposable (Graßmann), multi-vectors and later extended by bilinearity. The Hestenesian ’dot’ product, extending the one-vector scalar product, is even worse having exceptions for scalars and the need...
متن کاملClifford geometric parameterization of inequivalent vacua
We propose a geometric method to parameterize inequivalent vacua by dynamical data. Introducing quantum Clifford algebras with arbitrary bilinear forms we distinguish isomorphic algebras –as Clifford algebras– by different filtrations resp. induced gradings. The idea of a vacuum is introduced as the unique algebraic projection on the base field embedded in the Clifford algebra, which is however...
متن کامل