Showing papers by "Harald Grosse published in 1995"
TL;DR: In this article, the authors describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly.
Abstract: Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product.
209 citations
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TL;DR: In this paper, the authors describe a self-interacting scalar field on the truncated sphere and perform the quantization using the functional (path) integral approach, and explicitely show that the model is finite and the UV-regularization automatically takes place.
Abstract: We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect to the isometries of the sphere. We explicitely show that the model is finite and the UV-regularization automatically takes place.
93 citations
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TL;DR: In this article, the Fuzzy sphere and a way to approximate topological nontrivial configurations using matrix models were presented, and an ultraviolet cut off procedure was obtained, which respects the symmetries of the model.
Abstract: We review recent progress in formulating two-dimensional models over noncommutative manifolds where the space-time coordinates enter in the formalism as non-commuting matrices. We describe the Fuzzy sphere and a way to approximate topological nontrivial configurations using matrix models. We obtain an ultraviolet cut off procedure, which respects the symmetries of the model. The treatment of spinors results from a supersymmetric formulation; our cut off procedure preserves even the supersymmetry.
15 citations
TL;DR: In this paper, the authors describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere, and the corresponding field theory actions conserve all basic symmetries of the standard commutative version.
Abstract: 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 symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only finite number of modes.
6 citations
TL;DR: A lattice-type regularization of supersymmetric field theories on a supersphere was constructed by approximating the ring of scalar superfields by an integer-valued sequence of finite dimensional rings of supermatrices and by using the differencial calculus of non-commutative geometry as mentioned in this paper.
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 dimensional rings of supermatrices and by using the differencial calculus of non-commutative geometry. The regulated theory involves only finite number of degrees of freedom and is manifestly supersymmetric.
6 citations
01 Jan 1995
TL;DR: In this paper, the Fuzzy sphere and a way to approximate topological nontrivial configurations using matrix models were presented, and an ultraviolet cut off procedure was obtained, which respects the symmetries of the model.
Abstract: We review recent progress in formulating two-dimensional models over noncommutative manifolds where the space-time coordinates enter in the formalism as non-commuting matrices. We describe the Fuzzy sphere and a way to approximate topological nontrivial configurations using matrix models. We obtain an ultraviolet cut off procedure, which respects the symmetries of the model. The treatment of spinors results from a supersymmetric formulation; our cut off procedure preserves even the supersymmetry.
6 citations