318 research outputs found
Extending invariant complex structures
We study the problem of extending a complex structure to a given Lie algebra
g, which is firstly defined on an ideal h of g. We consider the next
situations: h is either complex or it is totally real. The next question is to
equip g with an additional structure, such as a (non)-definite metric or a
symplectic structure and to ask either h is non-degenerate, isotropic, etc.
with respect to this structure, by imposing a compatibility assumption. We show
that this implies certain constraints on the algebraic structure of g.
Constructive examples illustrating this situation are shown, in particular
computations in dimension six are given.Comment: 22 pages, plus an Addendu
The role of magnetoplasmons in Casimir force calculations
In this paper we review the role of magneto plasmon polaritons in the Casimir
force calculations. By applying an external constant magnetic field a strong
optical anisotropy is induced on two parallel slabs reducing the reflectivity
and thus the Casimir force. As the external magnetic field increases, the
Casimir force decreases. Thus, with an an external magnetic field the Casimir
force can be controlled.The calculations are done in the Voigt configuration
where the magnetic field is parallel to the slabs. In this configuration the
reflection coefficients for TE and TM modes do not show mode conversion.Comment: contribution to QFEXT09, Norman, Oklahoma 200
Small oscillations and the Heisenberg Lie algebra
The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems
for quadratic Hamiltonians of on coadjoint orbits of the
Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie
algebra that admits an ad-invariant metric. Its quadratic induces
the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that
one on . This system is a Lax pair equation whose solution can
be computed with help of the Adjoint representation. For a certain class of
functions, the Poisson commutativity on the coadjoint orbits in
is related to the commutativity of a family of derivations of the
2n+1-dimensional Heisenberg Lie algebra . Therefore the complete
integrability is related to the existence of an n-dimensional abelian
subalgebra of certain derivations in . For instance, the motion
of n-uncoupled harmonic oscillators near an equilibrium position can be
described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of
the AKS schem
Lanczos Spintensor via the Andersson-Edgar’s Generator
For arbitrary geometries with Petrov types O, N, III, and D (empty), we construct the Andersson-Edgar’s generator for the Lanczos spinor
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