911 research outputs found
Does antimatter emit a new light ?
We identify a number of problematic aspects of current classical and quantum
theories of antimatter; we introduce a new mathematical formalism which is an
antiautomorphic image of that of matter equivalent to charge conjugation at the
operator level, but applicable from Newton's equations to quantum mechanics; we
show that the emerging new theory of antimatter recovers known experimental
data on electroweak interactions; we finally identity the following predictions
of the theory: 1) reversal in the field of matter of the gravitational
curvature (antigravity) for stable antiparticles and their bound states, such
as the anti-hydrogen atom; 2) conventional (attractive) gravity for a bound
state of an elementary particle and its antiparticle, such as the positronium;
and 3) prediction that the anti- hydrogen atom emits a new photon which
coincides with the conventional photon for all electroweak interactions but
experiences repulsion in the gravitational field of matter.Comment: 18 pages, TEX, in press at Hyperfine Inte
Representations of the cyclically symmetric q-deformed algebra
An algebra homomorphism from the nonstandard q-deformed (cyclically
symmetric) algebra to the extension of the Hopf
algebra is constructed. Not all irreducible representations of
can be extended to representations of . Composing
the homomorphism with irreducible representations of
we obtain representations of . Not all of these representations of
are irreducible. Reducible representations of are
decomposed into irreducible components. In this way we obtain all irreducible
representations of when is not a root of unity. A part of these
representations turns into irreducible representations of the Lie algebra
so when . Representations of the other part have no classical
analogue. Using the homomorphism it is shown how to construct tensor
products of finite dimensional representations of . Irreducible
representations of when is a root of unity are constructed.
Part of them are obtained from irreducible representations of by means of the homomorphism .Comment: 28 pages, LaTe
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
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