20,350 research outputs found
On Curvature in Noncommutative Geometry
A general definition of a bimodule connection in noncommutative geometry has
been recently proposed. For a given algebra this definition is compared with
the ordinary definition of a connection on a left module over the associated
enveloping algebra. The corresponding curvatures are also compared.Comment: 16 pages, PlainTe
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
Linear connections on matrix geometries
A general definition of a linear connection in noncommutative geometry has
been recently proposed. Two examples are given of linear connections in
noncommutative geometries which are based on matrix algebras. They both possess
a unique metric connection.Comment: 14p, LPTHE-ORSAY 94/9
Linear Connections in Non-Commutative Geometry
A construction is proposed for linear connections on non-commutative
algebras. The construction relies on a generalisation of the Leibnitz rules of
commutative geometry and uses the bimodule structure of . A special
role is played by the extension to the framework of non-commutative geometry of
the permutation of two copies of . The construction of the linear
connection as well as the definition of torsion and curvature is first proposed
in the setting of the derivations based differential calculus of Dubois-
Violette and then a generalisation to the framework proposed by Connes as well
as other non-commutative differential calculi is suggested. The covariant
derivative obtained admits an extension to the tensor product of several copies
of . These constructions are illustrated with the example of the
algebra of matrices.Comment: 15 pages, LMPM ../94 (uses phyzzx
On the first order operators in bimodules
We analyse the structure of the first order operators in bimodules introduced
by A. Connes. We apply this analysis to the theory of connections on bimodules
generalizing thereby several proposals.Comment: 13 pages, AMSLaTe
Examples of derivation-based differential calculi related to noncommutative gauge theories
Some derivation-based differential calculi which have been used to construct
models of noncommutative gauge theories are presented and commented. Some
comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour
of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry,
Homology and Fundamental Interactions". To appear in a special issue of
International Journal of Geometric Methods in Modern Physic
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
Complex structures and the Elie Cartan approach to the theory of spinors
Each isometric complex structure on a 2-dimensional euclidean space
corresponds to an identification of the Clifford algebra of with the
canonical anticommutation relation algebra for ( fermionic) degrees of
freedom. The simple spinors in the terminology of E.~Cartan or the pure spinors
in the one of C. Chevalley are the associated vacua. The corresponding states
are the Fock states (i.e. pure free states), therefore, none of the above
terminologies is very good.Comment: 10
BRS Cohomology of the Supertranslations in D=4
Supersymmetry transformations are a kind of square root of spacetime
translations. The corresponding Lie superalgebra always contains the
supertranslation operator . We find that the
cohomology of this operator depends on a spin-orbit coupling in an SU(2) group
and has a quite complicated structure. This spin-orbit type coupling will turn
out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9
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