83 research outputs found
Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
The effects of noncommutativity and of the existence of a minimal length on
the phase space of a dilatonic cosmological model are investigated. The
existence of a minimum length, results in the Generalized Uncertainty Principle
(GUP), which is a deformed Heisenberg algebra between the minisuperspace
variables and their momenta operators. We extend these deformed commutating
relations to the corresponding deformed Poisson algebra. For an exponential
dilaton potential, the exact classical and quantum solutions in the commutative
and noncommutative cases, and some approximate analytical solutions in the case
of GUP, are presented and compared.Comment: 16 pages, 3 figures, typos correcte
Self-dual Einstein Spaces, Heavenly Metrics and Twistors
Four-dimensional quaternion-Kahler metrics, or equivalently self-dual
Einstein spaces M, are known to be encoded locally into one real function h
subject to Przanowski's Heavenly equation. We elucidate the relation between
this description and the usual twistor description for quaternion-Kahler
spaces. In particular, we show that the same space M can be described by
infinitely many different solutions h, associated to different complex (local)
submanifolds on the twistor space, and therefore to different (local)
integrable complex structures on M. We also study quaternion-Kahler
deformations of M and, in the special case where M has a Killing vector field,
show that the corresponding variations of h are related to eigenmodes of the
conformal Laplacian on M. We exemplify our findings on the four-sphere S^4, the
hyperbolic plane H^4 and on the "universal hypermultiplet", i.e. the
hypermultiplet moduli space in type IIA string compactified on a rigid
Calabi-Yau threefold.Comment: 44 pages, 1 figure; misprints correcte
Multidimensional integrable systems and deformations of Lie algebra homomorphisms
We use deformations of Lie algebra homomorphisms to construct deformations of
dispersionless integrable systems arising as symmetry reductions of
anti--self--dual Yang--Mills equations with a gauge group Diff.Comment: 14 pages. An example of a reduction to the Beltrami equation added.
New title. Final version, published in JM
-SDYM Fields and Heavenly Spaces. I. -SDYM equations as an integrable system
It is shown that the self-dual Yang-Mills (SDYM) equations for the
-bracket Lie algebra on a heavenly space can be reduced to one equation
(the \it master equation\rm). Two hierarchies of conservation laws for this
equation are constructed. Then the twistor transform and a solution to the
Riemann-Hilbert problem are given.Comment: 25 page
-SDYM fields and heavenly spaces: II. Reductions of the -SDYM system
Reductions of self-dual Yang-Mills (SDYM) system for -bracket Lie
algebra to the Husain-Park (HP) heavenly equation and to
sl(N,{\boldmath{C}) SDYM equation are given. An example of a sequence of
chiral fields () tending for to a curved heavenly
space is found.Comment: 18 page
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