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The construction of noncommutative manifolds using coherent states
We describe the construction of noncommutative manifolds, which are the noncommutative analogs of homogeneous spaces using coherent states. In the commutative limit, we obtain standard manifolds.
Field Theory on a Supersymmetric Lattice
Abstract: A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integer-valued sequence of finite
Finite quantum field theory in noncommutative geometry
We describe a self-interacting scalar field on a truncated sphere and perform the quantization using the functional (path) integral approach. The theory possesses full symmetry with respect to the
The dirac operator on the fuzzy sphere
We introduce the fuzzy analog of spinor bundles over the sphere on which the noncommutative analog of the Dirac operator acts. We construct the complete set of eigenstates including zero modes. In
Topologically nontrivial field configurations in noncommutative geometry
In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic
The origin of chiral anomaly and the noncommutative geometry
We describe scalar and spinor fields on a noncommutative sphere starting from canonical realizations of the enveloping algebra A=U(u(2)). The gauge extension of a free spinor model, the Schwinger
On finite 4D quantum field theory in non-commutative geometry
The truncated 4-dimensional sphereS4 and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping theSO(5)
Space-time noncommutativity, discreteness of time and unitarity
Abstract. Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences they still violate unitarity, while