153 research outputs found
On Poisson Structure and Curvature
We consider a curved space-time whose algebra of functions is the commutative
limit of a noncommutative algebra and which has therefore an induced Poisson
structure. In a simple example we determine a relation between this structure
and the Riemann tensor.Comment: 8 pages, Late
Noncommutative de Sitter and FRW spaces
Several versions of fuzzy four-dimensional de Sitter space are constructed
using the noncommutative frame formalism. Although all noncommutative
spacetimes which are found have commutative de Sitter metric as a classical
limit, the algebras and the differential calculi which define them have many
differences which we derive and discuss.Comment: 20 page
On noncommutative spherically symmetric spaces
Two families of noncommutative extensions are given of a general space-time
metric with spherical symmetry, both based on the matrix truncation of the
functions on the sphere of symmetry. The first family uses the truncation to
foliate space as an infinite set of spheres, is of dimension four and
necessarily time-dependent; the second can be time-dependent or static, is of
dimension five and uses the truncation to foliate the internal space.Comment: 22 page
Leibniz Rules and Reality Conditions
An analysis is made of reality conditions within the context of
noncommutative geometry. We show that if a covariant derivative satisfies a
given left Leibniz rule then a right Leibniz rule is equivalent to the reality
condition. We show also that the matrix which determines the reality condition
must satisfy the Yang-Baxter condition if the extension of the covariant
derivative to tensor products is to satisfy the reality condition. This is
equivalent to the braid condition for the matrix which determines the right
Leibniz rule.Comment: 13 pages, LaTeX2
The Hidden Geometry of the Quantum Euclidean Space
We briefly describe how to introduce the basic notions of noncommutative
differential geometry on the 3-dim quantum space covariant under the quantum
group of rotations .Comment: latex file, 9 pages, no figure. Talk given at QGS98, Pragu
WKB Approximation in Noncommutative Gravity
We consider the quasi-commutative approximation to a noncommutative geometry
defined as a generalization of the moving frame formalism. The relation which
exists between noncommutativity and geometry is used to study the properties of
the high-frequency waves on the flat background.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Alien Registration- Madore, John (Fort Fairfield, Aroostook County)
https://digitalmaine.com/alien_docs/36522/thumbnail.jp
External Fields as Intrinsic Geometry
There is an interesting dichotomy between a space-time metric considered as
external field in a flat background and the same considered as an intrinsic
part of the geometry of space-time. We shall describe and compare two other
external fields which can be absorbed into an appropriate redefinition of the
geometry, this time a noncommutative one. We shall also recall some previous
incidences of the same phenomena involving bosonic field theories. It is known
that some such theories on the commutative geometry of space-time can be
re-expressed as abelian-gauge theory in an appropriate noncommutative geometry.
The noncommutative structure can be considered as containing extra modes all of
whose dynamics are given by the one abelian action.Comment: 19 pages, Late
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