3 research outputs found
Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices
Isotopic liftings of algebraic structures are investigated in the context of
Clifford algebras, where it is defined a new product involving an arbitrary,
but fixed, element of the Clifford algebra. This element acts as the unit with
respect to the introduced product, and is called isounit. We construct
isotopies in both associative and non-associative arbitrary algebras, and
examples of these constructions are exhibited using Clifford algebras, which
although associative, can generate the octonionic, non-associative, algebra.
The whole formalism is developed in a Clifford algebraic arena, giving also the
necessary pre-requisites to introduce isotopies of the exterior algebra. The
flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact,
when the generators of the isotopic Lie algebra su(6) are constructed, and the
unit of the isotopic Clifford algebra is shown to be a function of the six
quark masses. The limits constraining the parameters, that are entries of the
representation of the isounit in the isotopic group SU(6), are based on the
most recent limits imposed on quark masses.Comment: 19 page
Isotopic Grand Unification with the Inclusion of Gravity (revised version)
We introduce a dual lifting of unified gauge theories, the first
characterized by the isotopies, which are axiom- preserving maps into broader
structures with positive-definite generalized units used for the representation
of matter under the isotopies of the Poincare' symmetry, and the second
characterized by the isodualities, which are anti-isomorphic maps with
negative-definite generalized units used for the representation of antimatter
under the isodualities of the Poincare' symmetry. We then submit, apparently
for the first time, a novel grand unification with the inclusion of gravity for
matter embedded in the generalized positive-definite units of unified gauge
theories while gravity for antimatter is embedded in the isodual isounit. We
then show that the proposed grand unification provides realistic possibilities
for a resolution of the axiomatic incompatibilities between gravitation and
electroweak interactions due to curvature, antimatter and the fundamental
space-time symmetries.Comment: 20 pages, Latex, revised in various details and with added reference