by V. V. Varlamov (Submitted on 26 Jul 2012)
Abstract: Supergroups are defined in the framework of $\dZ_2$-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups related with the modulo 2 and modulo 8 periodicities of the complex and real Clifford algebras. Particle (fermionic and bosonic) representations of a universal covering (spinor group $\spin_+(1,3)$) of the proper orthochronous Lorentz group are constructed via the Clifford algebra formalism. Complex and real supergroups are defined on the representation system of $\spin_+(1,3)$. It is shown that a cyclic (modulo 2) structure of the complex supergroup is equivalent to a supersymmetric action, that is, it converts fermionic representations into bosonic representations and vice versa. The cyclic action of the real supergroup leads to a much more high-graded symmetry related with the modulo 8 periodicity of the real Clifford algebras. This symmetry acts on the system of real representations of $\spin_+(1,3)$.
|Comments:||22 pages. arXiv admin note: substantial text overlap with arXiv:1107.4156, arXiv:math-ph/0203059, arXiv:math-ph/0108022, arXiv:math-ph/0405040|
|Subjects:||Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)|
|Cite as:||arXiv:1207.6162v1 [math-ph]|
Source: Email by C. Castro, 3 Aug. 2012, perelmanc_at_hotmail.com, http://arxiv.org/abs/1207.6162