643 research outputs found
Noncommutative integrability and recursion operators
Geometric structures underlying commutative and non commutative integrable
dynamics are analyzed. They lead to a new characterization of noncommutative
integrability in terms of spectral properties and of Nijenhuis torsion of an
invariant (1,1) tensor field. The construction of compatible symplectic
structures is also discussed.Comment: 20 pages, LaTex, no figure
Vacuum Einstein metrics with bidimensional Killing leaves. I-Local aspects
The solutions of vacuum Einstein's field equations, for the class of
Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing
fields, are explicitly described. They are parametrized either by solutions of
a transcendental equation (the tortoise equation), or by solutions of a linear
second order differential equation in two independent variables. Metrics,
corresponding to solutions of the tortoise equation, are characterized as those
that admit a 3-dimensional Lie algebra of Killing fields with bidimensional
leaves.Comment: LateX file, 33 pages, 2 figure
The gravity of light
A solution of the old problem raised by Tolman, Ehrenfest, Podolsky and
Wheeler, concerning the lack of attraction of two light pencils "moving
parallel", is proposed, considering that the light can be source of nonlinear
gravitational waves corresponding (in the would be quantum theory of gravity)
to spin-1 massless particles.Comment: Style is changed in standard latex, abstract has been reduced and the
order of sections has been change
Alternative Canonical Formalism for the Wess-Zumino-Witten Model
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model
which depends on two integer parameters rather than one. The usual theory can
be obtained as a contraction, in which our two parameters go to infinity
keeping the difference fixed. The quantum theory is equivalent to a generalized
Thirring model, with left and right handed fermions transforming under
different representations of the symmetry group. We also point out that the
classical WZW model with a compact target space has a canonical formalism in
which the current algebra is an affine Lie algebra of non--compact type.
Also, there are some non--unitary quantizations of the WZW model in which
there is invariance only under half the conformal algebra (one copy of the
Virasoro algebra).Comment: 22 pages; UR-133
Inflationary Cosmology from Noncommutative Geometry
In the framework of the Connes-Lott model based on noncommutative geometry,
the basic features of a gauge theory in the presence of gravity are reviewed,
in order to show the possible physical relevance of this scheme for
inflationary cosmology. These models naturally contain at least two scalar
fields, interacting with each other whenever more than one fermion generation
is assumed. In this paper we propose to investigate the behaviour of these two
fields (one of which represents the distance between the copies of a
two-sheeted space-time) in the early stages of the universe evolution. In
particular the simplest abelian model, which preserves the main characteristics
of more complicate gauge theories, is considered and the corresponding
inflationary dynamics is studied. We find that a chaotic inflation is naturally
favoured, leading to a field configuration in which no symmetry breaking occurs
and the final distance between the two sheets of space-time is smaller the
greater the number of -fold in each sheet.Comment: 29 pages, plain Latex, + 2 figures as uuencoded postscript files,
substantially revised version to appear in the Int. Jour. Mod. Phys.
Constraints on Unified Gauge Theories from Noncommutative Geometry
The Connes and Lott reformulation of the strong and electroweak model
represents a promising application of noncommutative geometry. In this scheme
the Higgs field naturally appears in the theory as a particular `gauge boson',
connected to the discrete internal space, and its quartic potential, fixed by
the model, is not vanishing only when more than one fermion generation is
present. Moreover, the exact hypercharge assignments and relations among the
masses of particles have been obtained. This paper analyzes the possibility of
extensions of this model to larger unified gauge groups. Noncommutative
geometry imposes very stringent constraints on the possible theories, and
remarkably, the analysis seems to suggest that no larger gauge groups are
compatible with the noncommutative structure, unless one enlarges the fermionic
degrees of freedom, namely the number of particles.Comment: 18 pages, Plain LaTeX, no figure
Spin-1 gravitational waves and their natural sources
Non-vacuum exact gravitational waves invariant for a non Abelian
two-dimensional Lie algebra generated by two Killing fields whose commutator is
of light type, are described. The polarization of these waves, already known
from previous works, is related to the sources. Non vacuum exact gravitational
waves admitting only one Killing field of light type are also discussed.Comment: 10 pages, late
Dynamical Aspects of Lie--Poisson Structures
Quantum Groups can be constructed by applying the quantization by deformation
procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to
develop an understanding of these structures by investigating dynamical systems
which are associated with this bracket. We look at and , as
submanifolds of a 4--dimensional phase space with constraints, and deal with
two classes of problems. In the first set of examples we consider some
hamiltonian systems associated with Lie-Poisson structures and we investigate
the equations of the motion. In the second set of examples we consider systems
which preserve the chosen bracket, but are dissipative. However in this
approach, they survive the quantization procedure.Comment: 17 pages, figures not include
Mirror Fermions in Noncommutative Geometry
In a recent paper we pointed out the presence of extra fermionic degrees of
freedom in a chiral gauge theory based on Connes Noncommutative Geometry. Here
we propose a mechanism which provides a high mass to these mirror states, so
that they decouple from low energy physics.Comment: 7 pages, LaTe
Gravitational fields with a non Abelian bidimensional Lie algebra of symmetries
Vacuum gravitational fields invariant for a bidimensional non Abelian Lie
algebra of Killing fields, are explicitly described. They are parameterized
either by solutions of a transcendental equation (the tortoise equation) or by
solutions of a linear second order differential equation on the plane.
Gravitational fields determined via the tortoise equation, are invariant for a
3-dimensional Lie algebra of Killing fields with bidimensional leaves. Global
gravitational fields out of local ones are also constructed.Comment: 8 pagese, latex, no figure
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