796 research outputs found
Quaternion-Octonion SU(3) Flavor Symmetry
Starting with the quaternionic formulation of isospin SU(2) group, we have
derived the relations for different components of isospin with quark states.
Extending this formalism to the case of SU(3) group we have considered the
theory of octonion variables. Accordingly, the octonion splitting of SU(3)
group have been reconsidered and various commutation relations for SU(3) group
and its shift operators are also derived and verified for different iso-spin
multiplets i.e. I, U and V- spins.
Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices
PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and
models of strong and electroweak interaction
Quaternion Octonion Reformulation of Quantum Chromodynamics
We have made an attempt to develop the quaternionic formulation of Yang -
Mill's field equations and octonion reformulation of quantum chromo dynamics
(QCD). Starting with the Lagrangian density, we have discussed the field
equations of SU(2) and SU(3) gauge fields for both cases of global and local
gauge symmetries. It has been shown that the three quaternion units explain the
structure of Yang- Mill's field while the seven octonion units provide the
consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics
Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators
An attempt has been made to investigate the global SU(2) and SU(3) unitary
flavor symmetries systematically in terms of quaternion and octonion
respectively. It is shown that these symmetries are suitably handled with
quaternions and octonions in order to obtain their generators, commutation
rules and symmetry properties. Accordingly, Casimir operators for SU(2)and
SU(3) flavor symmetries are also constructed for the proper testing of these
symmetries in terms of quaternions and octonions
Octonion Quantum Chromodynamics
Starting with the usual definitions of octonions, an attempt has been made to
establish the relations between octonion basis elements and Gell-Mann \lambda
matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann
\lambda matrices of SU(3)symmetry and octonion basis elements. Consequently,
the quantum chromo dynamics (QCD) has been reformulated and it is shown that
the theory of strong interactions could be explained better in terms of
non-associative octonion algebra. Further, the octonion automorphism group
SU(3) has been suitably handled with split basis of octonion algebra showing
that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields
which are responsible for the existence of two gauge potentials respectively
associated with electric charge and magnetic monopole and supports well the
idea that the colored quarks are dyons
Rotation measure variations for 20 millisecond pulsars
We report on variations in the mean position angle of the 20 millisecond
pulsars being observed as part of the Parkes Pulsar Timing Array (PPTA)
project. It is found that the observed variations are dominated by changes in
the Faraday rotation occurring in the Earth's ionosphere. Two ionospheric
models are used to correct for the ionospheric contribution and it is found
that one based on the International Reference Ionosphere gave the best results.
Little or no significant long-term variation in interstellar RM was found with
limits typically about 0.1 rad m yr in absolute value. In a few
cases, apparently significant RM variations over timescales of a few 100 days
or more were seen. These are unlikely to be due to localised magnetised regions
crossing the line of sight since the implied magnetic fields are too high. Most
probably they are statistical fluctuations due to random spatial and temporal
variations in the interstellar electron density and magnetic field along the
line of sight.Comment: Accepted for publication in Astrophysics & Space Scienc
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
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