1,698 research outputs found
Fuzzy Space-Time
A review is made of recent efforts to define linear connections and their
corresponding curvature within the context of noncommutative geometry. As an
application it is suggested that it is possible to identify the gravitational
field as a phenomenological manifestation of space-time commutation relations
and to thereby clarify its role as an ultraviolet regularizer.Comment: 17 pages LaTe
Quantum Space-time and Classical Gravity
A method has been recently proposed for defining an arbitrary number of
differential calculi over a given noncommutative associative algebra. As an
example a version of quantized space-time is considered here. It is found that
there is a natural differential calculus using which the space-time is
necessarily flat Minkowski space-time. Perturbations of this calculus are shown
to give rise to non-trivial gravitational fields.Comment: 21 pages LaTe
Fuzzy Surfaces of Genus Zero
A fuzzy version of the ordinary round 2-sphere has been constructed with an
invariant curvature. We here consider linear connections on arbitrary fuzzy
surfaces of genus zero. We shall find as before that they are more or less
rigidly dependent on the differential calculus used but that a large number of
the latter can be constructed which are not covariant under the action of the
rotation group. For technical reasons we have been forced to limit our
considerations to fuzzy surfaces which are small perturbations of the fuzzy
sphere.Comment: 11 pages, Late
Linear Connections on Fuzzy Manifolds
Linear connections are introduced on a series of noncommutative geometries
which have commutative limits. Quasicommutative corrections are calculated.Comment: 10 pages PlainTex; LPTHE Orsay 95/42; ESI Vienna 23
Classical Gravity on Fuzzy Space-Time
A review is made of recent efforts to find relations between the commutation
relations which define a noncommutative geometry and the gravitational field
which remains as a shadow in the commutative limit.Comment: Lecture given at the 30th International Symposium Ahrenshoop on the
Theory of Elementary Particles, Buckow, Germany, August 27-31, 1996; 11 Pages
LaTe
Deformations of Differential Calculi
It has been suggested that quantum fluctuations of the gravitational field
could give rise in the lowest approximation to an effective noncommutative
version of Kaluza-Klein theory which has as extra hidden structure a
noncommutative geometry. It would seem however from the Standard Model, at
least as far as the weak interactions are concerned, that a double-sheeted
structure is the phenomenologically appropriate one at present accelerator
energies. We examine here to what extent this latter structure can be
considered as a singular limit of the former.Comment: 11 pages of Late
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