418 research outputs found
Deforming the Maxwell-Sim Algebra
The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in
which the momentum generators no longer commute, but satisfy
. The charges commute with the momenta,
and transform tensorially under the action of the angular momentum generators.
If one constructs an action for a massive particle, invariant under these
symmetries, one finds that it satisfies the equations of motion of a charged
particle interacting with a constant electromagnetic field via the Lorentz
force. In this paper, we explore the analogous constructions where one starts
instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra
of Very Special Relativity. It admits an analogous non-central extension, and
we find that a particle action invariant under this Maxwell-Sim algebra again
describes a particle subject to the ordinary Lorentz force. One can also deform
the ISim algebra to DISim, where is a non-trivial dimensionless
parameter. We find that the motion described by an action invariant under the
corresponding Maxwell-DISim algebra is that of a particle interacting via a
Finslerian modification of the Lorentz force.Comment: Appendix on Lifshitz and Schrodinger algebras adde
Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras
A family of deformed Hopf algebras corresponding to the classical maximal
isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous
algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to
have a bicrossproduct structure. This is done for both the algebra and, in a
low-dimensional example, for the (dual) group aspects of the deformation.Comment: LaTeX file, 20 pages. Trivial changes. To appear in J. Phys.
Disclinations, dislocations and continuous defects: a reappraisal
Disclinations, first observed in mesomorphic phases, are relevant to a number
of ill-ordered condensed matter media, with continuous symmetries or frustrated
order. They also appear in polycrystals at the edges of grain boundaries. They
are of limited interest in solid single crystals, where, owing to their large
elastic stresses, they mostly appear in close pairs of opposite signs. The
relaxation mechanisms associated with a disclination in its creation, motion,
change of shape, involve an interplay with continuous or quantized dislocations
and/or continuous disclinations. These are attached to the disclinations or are
akin to Nye's dislocation densities, well suited here. The notion of 'extended
Volterra process' takes these relaxation processes into account and covers
different situations where this interplay takes place. These concepts are
illustrated by applications in amorphous solids, mesomorphic phases and
frustrated media in their curved habit space. The powerful topological theory
of line defects only considers defects stable against relaxation processes
compatible with the structure considered. It can be seen as a simplified case
of the approach considered here, well suited for media of high plasticity
or/and complex structures. Topological stability cannot guarantee energetic
stability and sometimes cannot distinguish finer details of structure of
defects.Comment: 72 pages, 36 figure
Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry
A new method to obtain trigonometry for the real spaces of constant curvature
and metric of any (even degenerate) signature is presented. The method
encapsulates trigonometry for all these spaces into a single basic
trigonometric group equation. This brings to its logical end the idea of an
absolute trigonometry, and provides equations which hold true for the nine
two-dimensional spaces of constant curvature and any signature. This family of
spaces includes both relativistic and non-relativistic homogeneous spacetimes;
therefore a complete discussion of trigonometry in the six de Sitter,
minkowskian, Newton--Hooke and galilean spacetimes follow as particular
instances of the general approach. Any equation previously known for the three
classical riemannian spaces also has a version for the remaining six
spacetimes; in most cases these equations are new. Distinctive traits of the
method are universality and self-duality: every equation is meaningful for the
nine spaces at once, and displays explicitly invariance under a duality
transformation relating the nine spaces. The derivation of the single basic
trigonometric equation at group level, its translation to a set of equations
(cosine, sine and dual cosine laws) and the natural apparition of angular and
lateral excesses, area and coarea are explicitly discussed in detail. The
exposition also aims to introduce the main ideas of this direct group
theoretical way to trigonometry, and may well provide a path to systematically
study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe
Volumes of polytopes in spaces of constant curvature
We overview the volume calculations for polyhedra in Euclidean, spherical and
hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary
tetrahedron in and . We also present some results, which provide a
solution for Seidel problem on the volume of non-Euclidean tetrahedron.
Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle,
horocycle or one branch of equidistant curve. This is a natural hyperbolic
analog of the cyclic quadrilateral in the Euclidean plane. We find a few
versions of the Brahmagupta formula for the area of such quadrilateral. We also
present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference
Progress in Classical and Quantum Variational Principles
We review the development and practical uses of a generalized Maupertuis
least action principle in classical mechanics, in which the action is varied
under the constraint of fixed mean energy for the trial trajectory. The
original Maupertuis (Euler-Lagrange) principle constrains the energy at every
point along the trajectory. The generalized Maupertuis principle is equivalent
to Hamilton's principle. Reciprocal principles are also derived for both the
generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis
Principle is the classical limit of Schr\"{o}dinger's variational principle of
wave mechanics, and is also very useful to solve practical problems in both
classical and semiclassical mechanics, in complete analogy with the quantum
Rayleigh-Ritz method. Classical, semiclassical and quantum variational
calculations are carried out for a number of systems, and the results are
compared. Pedagogical as well as research problems are used as examples, which
include nonconservative as well as relativistic systems
Loitering with intent: dealing with human-intensive systems
This paper discusses the professional roles of information systems analysts and users, focusing on a perspective of human intensive, rather than software intensive information systems. The concept of ‘meaningful use’ is discussed in re-lation to measures of success/failure in IS development. The authors consider how a number of different aspects of reductionism may distort analyses, so that processes of inquiry cannot support organizational actors to explore and shape their requirements in relation to meaningful use. Approaches which attempt to simplify complex problem spaces, to render them more susceptible to ‘solution’ are problematized. Alternative perspectives which attempt a systematic, holistic complexification, by supporting contextual dependencies to emerge, are advocated as a way forward
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