560 research outputs found
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
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
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
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
Nonlinear gravitational waves and their polarization
Vacuum gravitational fields invariant for a non Abelian Lie algebra generated
by two Killing fields whose commutator is light-like are analyzed. It is shown
that they represent nonlinear gravitational waves obeying to two nonlinear
superposition laws. The energy and the polarization of this family of waves are
explicitely evaluated.Comment: 9 pages. LateX. Minor correction
Lattices and Their Continuum Limits
We address the problem of the continuum limit for a system of Hausdorff
lattices (namely lattices of isolated points) approximating a topological space
. The correct framework is that of projective systems. The projective limit
is a universal space from which can be recovered as a quotient. We dualize
the construction to approximate the algebra of continuous
functions on . In a companion paper we shall extend this analysis to systems
of noncommutative lattices (non Hausdorff lattices).Comment: 11 pages, 1 Figure included in the LaTeX Source New version, minor
modifications (typos corrected) and a correction in the list of author
Distances on a Lattice from Non-commutative Geometry
Using the tools of noncommutative geometry we calculate the distances between
the points of a lattice on which the usual discretized Dirac operator has been
defined. We find that these distances do not have the expected behaviour,
revealing that from the metric point of view the lattice does not look at all
as a set of points sitting on the continuum manifold. We thus have an
additional criterion for the choice of the discretization of the Dirac
operator.Comment: 14 page
Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
In this paper we study the structure of the Hilbert space for the recent
noncommutative geometry models of gauge theories. We point out the presence of
unphysical degrees of freedom similar to the ones appearing in lattice gauge
theories (fermion doubling). We investigate the possibility of projecting out
these states at the various levels in the construction, but we find that the
results of these attempts are either physically unacceptable or geometrically
unappealing.Comment: plain LaTeX, pp. 1
Noncommutative Lattices and Their Continuum Limits
We consider finite approximations of a topological space by
noncommutative lattices of points. These lattices are structure spaces of
noncommutative -algebras which in turn approximate the algebra \cc(M) of
continuous functions on . We show how to recover the space and the
algebra \cc(M) from a projective system of noncommutative lattices and an
inductive system of noncommutative -algebras, respectively.Comment: 22 pages, 8 Figures included in the LaTeX Source New version, minor
modifications (typos corrected) and a correction in the list of author
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