Symmetries in the hyperbolic Hilbert space

S. Ulrych
2005 Physics Letters B  
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
more » ... . 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.
doi:10.1016/j.physletb.2005.05.036 fatcat:wymfu5f4pjgr5aqmlkxioo2iyu