The generalized Clifford algebra and the unitary group

“Easy spin-symmetry-adaptation.” Exploitation of the Clifford algebra unitary group in correlated many-electron theories

An efficient scheme for the generation of spin-symmetry adapted matrix elements required by all correlated many electron wave function methods of electronic structure theory is briefly outlined. Matrix elements can be formulated in the Clifford algebra unitary group representation of Gel’fand-Tsetlin basis, Clifford-Weyl basis, Jeziorski-Paldus-Jankowski basis or determinant basis in order to e...

Unitary Units of the Group Algebra F2kQ8

g∈G agg −1 is an antiautomorphism of KG of order 2. An element v of V (KG) satisfying v = v is called unitary. We denote by V∗(KG) the subgroup of V (KG) formed by the unitary elements of KG. Let char(K) be the characteristic of the field K. In [2], A.Bovdi and A. Szákacs construct a basis for V∗(KG) where char(K) > 2. Also A. Bovdi and L. Erdei [1] determine the structure of V∗(F2G) for all gr...

Clifford Algebra of Spacetime and the Conformal Group

We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. A Clifford space (that contains spacetime, in particular) does not contain only points (events), but also lines, surfaces, volumes, etc.. All those geometric objects are very elegantly and compactly described by means of the geometric calculus based on Clifford algebra. A subgroup of the Clifford...

On Generalized Clifford Algebra C (n) 4 and GLq(2; C) Quantum Group A.K.Kwa´sniewski

Use of group theory and Clifford algebra in the study of generalized Dirac equation for particles with arbitrary spin

contains many of the features of the Dirac theory. The theory of spin-s free particles has been also developed by Proca [4], Kemmer [5] and Bargmann and Wigner [6]. All of these formalisms for spin-s free particles have many intrinsic contradictions and difficulties when an electromagnetic field interaction is introduced (see [7] and references therein). It should be noted that the mathematical...