The paper presents a multivector calculus within a Clifford algebra which is isomorphic to a tensor product of two quaternion algebras and thus differs from the corresponding complexified algebra used in the spacetime algebra approach (STA). Major symmetry groups of physics : the Lorentz group, the conformal group, the symplectic group and SU(4) are expressed within this Clifford algebra (taken over Ñ or Â). Physical applications such as the special theory of relativity, classical electromagnetism, Einstein's field equations and Dirac's equation (Dirac's algebra being represented by 2X2 matrices over complex quaternions) are discussed.

Patrick.Girard@cipcinsa.insa-lyon.fr