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The construction of noncommutative manifolds using coherent states

- H. Grosse, P. Prešnajder
- Mathematics
- 1 July 1993

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.… Expand

Field Theory on a Supersymmetric Lattice

- H. Grosse, C. Klimčík, P. Prešnajder
- Mathematics, Physics
- 13 July 1995

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… Expand

Finite quantum field theory in noncommutative geometry

- H. Grosse, C. Klimčík, P. Prešnajder
- Mathematics
- 1 February 1996

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… Expand

The dirac operator on the fuzzy sphere

- H. Grosse, P. Prešnajder
- Mathematics
- 1 February 1995

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… Expand

Quantum field theory on non-commutative space-times and the persistence of ultraviolet divergences

- M. Chaichian, A. Demichev, P. Prešnajder
- Physics
- 20 December 1998

Topologically nontrivial field configurations in noncommutative geometry

- H. Grosse, C. Klimčík, P. Prešnajder
- Mathematics
- 12 October 1995

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… Expand

The origin of chiral anomaly and the noncommutative geometry

- P. Prešnajder
- Mathematics
- 7 December 1999

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… Expand

q-deformations of Virasoro algebra and conformal dimensions

- M. Chaichian, A. P. Isaev, J. Lukierski, Z. Popowicz, P. Prešnajder
- Mathematics
- 13 June 1991

On finite 4D quantum field theory in non-commutative geometry

- H. Grosse, C. Klimčík, P. Prešnajder
- Physics
- 21 February 1996

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)… Expand

Space-time noncommutativity, discreteness of time and unitarity

- M. Chaichian, A. Demichev, P. Prešnajder, A. Tureanu
- Physics
- 19 July 2000

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… Expand

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