2,859 research outputs found
From Quantum Universal Enveloping Algebras to Quantum Algebras
The ``local'' structure of a quantum group G_q is currently considered to be
an infinite-dimensional object: the corresponding quantum universal enveloping
algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping
algebra of a n-dimensional Lie algebra g=Lie(G). However, we show how, by
starting from the generators of the underlying Lie bialgebra (g,\delta), the
analyticity in the deformation parameter(s) allows us to determine in a unique
way a set of n ``almost primitive'' basic objects in U_q(g), that could be
properly called the ``quantum algebra generators''. So, the analytical
prolongation (g_q,\Delta) of the Lie bialgebra (g,\delta) is proposed as the
appropriate local structure of G_q. Besides, as in this way (g,\delta) and
U_q(g) are shown to be in one-to-one correspondence, the classification of
quantum groups is reduced to the classification of Lie bialgebras. The su_q(2)
and su_q(3) cases are explicitly elaborated.Comment: 16 pages, 0 figures, LaTeX fil
A maximally superintegrable deformation of the N-dimensional quantum KeplerâCoulomb system
XXIst International Conference on Integrable Systems and Quantum Symmetries (ISQS21,) 12â16 June 2013, Prague, Czech RepublicThe N-dimensional quantum Hamiltonian
HË = â
~
2
|q|
2(η + |q|)
â
2 â
k
η + |q|
is shown to be exactly solvable for any real positive value of the parameter η. Algebraically,
this Hamiltonian system can be regarded as a new maximally superintegrable η-deformation
of the N-dimensional KeplerâCoulomb Hamiltonian while, from a geometric viewpoint, this
superintegrable Hamiltonian can be interpreted as a system on an N-dimensional Riemannian
space with nonconstant curvature. The eigenvalues and eigenfunctions of the model are explicitly
obtained, and the spectrum presents a hydrogen-like shape for positive values of the deformation
parameter η and of the coupling constant k
Twisted Conformal Algebra so(4,2)
A new twisted deformation, U_z(so(4,2)), of the conformal algebra of the
(3+1)-dimensional Minkowskian spacetime is presented. This construction is
provided by a classical r-matrix spanned by ten Weyl-Poincare generators, which
generalizes non-standard quantum deformations previously obtained for so(2,2)
and so(3,2). However, by introducing a conformal null-plane basis it is found
that the twist can indeed be supported by an eight-dimensional carrier
subalgebra. By construction the Weyl-Poincare subalgebra remains as a Hopf
subalgebra after deformation. Non-relativistic limits of U_z(so(4,2)) are shown
to be well defined and they give rise to new twisted conformal algebras of
Galilean and Carroll spacetimes. Furthermore a difference-differential massless
Klein-Gordon (or wave) equation with twisted conformal symmetry is constructed
through deformed momenta and position operators. The deformation parameter is
interpreted as the lattice step on a uniform Minkowskian spacetime lattice
discretized along two basic null-plane directions.Comment: 20 pages, LaTe
The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra
Using a contraction procedure, we construct a twist operator that satisfies a
shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2))
algebra. The corresponding universal matrix obeys a
Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a
class of representations, the dynamical Yang-Baxter equation may be expressed
as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure
Statistics of Core Lifetimes in Numerical Simulations of Turbulent, Magnetically Supercritical Molecular Clouds
We present measurements of the mean dense core lifetimes in numerical
simulations of magnetically supercritical, turbulent, isothermal molecular
clouds, in order to compare with observational determinations. "Prestellar"
lifetimes (given as a function of the mean density within the cores, which in
turn is determined by the density threshold n_thr used to define them) are
consistent with observationally reported values, ranging from a few to several
free-fall times. We also present estimates of the fraction of cores in the
"prestellar", "stellar'', and "failed" (those cores that redisperse back into
the environment) stages as a function of n_thr. The number ratios are measured
indirectly in the simulations due to their resolution limitations. Our approach
contains one free parameter, the lifetime of a protostellar object t_yso (Class
0 + Class I stages), which is outside the realm of the simulations. Assuming a
value t_yso = 0.46 Myr, we obtain number ratios of starless to stellar cores
ranging from 4-5 at n_thr = 1.5 x 10^4 cm^-3 to 1 at n_thr = 1.2 x 10^5 cm^-3,
again in good agreement with observational determinations. We also find that
the mass in the failed cores is comparable to that in stellar cores at n_thr =
1.5 x 10^4 cm^-3, but becomes negligible at n_thr = 1.2 x 10^5 cm^-3, in
agreement with recent observational suggestions that at the latter densities
the cores are in general gravitationally dominated. We conclude by noting that
the timescale for core contraction and collapse is virtually the same in the
subcritical, ambipolar diffusion-mediated model of star formation, in the model
of star formation in turbulent supercritical clouds, and in a model
intermediate between the previous two, for currently accepted values of the
clouds' magnetic criticality.Comment: 25 pages, 8 figures, ApJ accepted. Fig.1 animation is at
http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies/Galvan_etal07/Galvan_etal07.htm
Antiferromagnetism in four dimensions: search for non-triviality
We present antiferromagnetism as a mechanism capable of modifying
substantially the phase diagram and the critical behaviour of statistical
mechanical models. This is particularly relevant in four dimensions, due to the
connection between second order transition points and the continuum limit as a
quantum field theory. We study three models with an antiferromagnetic
interaction: the Ising and the O(4) Models with a second neighbour negative
coupling, and the \RP{2} Model. Different conclusions are obtained depending
on the model.Comment: 4 pages LateX. Contribution to Lat9
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