Symmetries in the hyperbolic Hilbert space

Details Symmetries in the hyperbolic Hilbert space Symmetries in the hyperbolic Hilbert space

2005-10-23

arxiv.org/abs/hep-th/0510199v1

Phys.Lett.B618:233-236,2005

Physics

High Energy Physics

High Energy Physics - Theory

5 pages Latex2e

Scientific paper

10.1016/j.physletb.2005.05.036

The Cl(3,0) Clifford algebra is represented with the commutative ring of hyperbolic numbers H. The canonical form of the Poincare mass operator defined in this vector space corresponds to a sixteen-dimensional structure. This conflicts with the natural perception of a four-dimensional space-time. The assumption that the generalized mass operator is an hermitian observable forms the basis of a mathematical model that decomposes the full sixteen-dimensional symmetry of the hyperbolic Hilbert space. The result is a direct product of the Lorentz group, the four-dimensional space-time, and the hyperbolic unitary group SU(4,H), which is considered as the internal symmetry of the relativistic quantum state. The internal symmetry is equivalent to the original form of the Pati-Salam model.

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