A. Stern

Generalized coherent state approach to star products and applications to the fuzzy sphere

We construct a star product associated with an arbitrary two dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. For the latter we need to define the “fuzzy” stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulas for the sphere.

Noncommutative Point Sources

We construct a perturbative solution to classical noncommutative gauge theory on R3 minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum mechanics of the noncommutative hydrogen atom gives shifts in the 1S hyperfine splitting which are first order in the noncommutativity parameter.

Noncommutative BTZ black hole and discrete time

We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values of the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the corresponding noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to symplectic leaves which are topologically , where is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.

Conformal edge currents in Chern-Simons theories

We develop elementary canonical methods for the quantization of Abelian and non-Abelian Chern-Simons actions, using well-known ideas in gauge theories and quantum gravity. Our approach does not involve choice of gauge or clever manipulations of functional integrals. When the spatial slice is a disc, it yields Witten’s edge states carrying a representation of the Kac-Moody algebra. The canonical expressions for the generators of diffeomorphisms on the boundary of the disc are also found, and it is established that they are the Chern-Simons version of the Sugawara construction. This paper is a prelude to our future publications on edge states, sources, vertex operators, and their spin and statistics in 3D and 4D topological field theories.

Space–time noncommutativity from particle mechanics

Abstract We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space–time noncommutativity. We show that there is an algebraic map from this gauge back to the standard ‘commuting’ gauge. Therefore the Poisson algebra, and the resulting quantum theory, are identical in the two gauges. The only difference is in the interpretation of space–time coordinates. The procedure is repeated for the case of a coupling with a constant electromagnetic field, where the reparametrization symmetry is preserved. For more arbitrary interactions, we show that standard dynamical system can be rendered noncommutative in space and time by a simple change of variables.

Snyder space revisited

Abstract We examine basis functions on momentum space for the three-dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO ( 3 ) group manifold, and that the basis functions span either one of two Hilbert spaces. This implies the existence of two distinct lattice structures of space. Continuous rotations and translations are unitarily implementable on these lattices.

Location and direction dependent effects in collider physics from noncommutativity

We examine the leading order noncommutative corrections to the differential and total cross sections for e{sup +}e{sup -{yields}}qq. After averaging over the Earths rotation, the results depend on the latitude for the collider, as well as the direction of the incoming beam. They also depend on the scale and direction of the noncommutativity. Using data from LEP, we exclude regions in the parameter space spanned by the noncommutative scale and angle relative to the Earths axis. We also investigate possible implications for phenomenology at the future International Linear Collider.

Particlelike solutions to classical noncommutative gauge theory

We construct perturbative static solutions to the classical field equations of noncommutative

Particle dynamics on Snyder space

U(1)

A New Class of Two-Dimensional Noncommutative Spaces

gauge theory for the three cases: (a) space-time noncommutativity, (b) space-space noncommutativity, and (c) both (a) and (b). The solutions tend to the Coulomb solution at spatial infinity and are valid for intermediate values of the radial coordinate