We show that a particular noncommutative geometry, sometimes called angular or $\rho$-Minkowski, requires the spectrum of time be discrete. In this space variable is not commuting with in cylindrical coordinates. The possible values can take go from minus infinity to plus infinity, equally spaced by scale noncommmutativity. Possible self-adjoint extensions "time operator" are discussed. They gi...

We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form. We use the action, due to Bergshoeff, London and Townsend, to study the noncommutativity properties of the boundary string coordinates. The constrained Hamiltonian formalism due to Dirac is used to derive the noncommutativity of coordinates. The chain of constraints is found to be ...

A large family of noncommutative Einstein-Maxwell null pp -waves to order one in the noncommutativity parameters is constructed. They are solutions to the Einstein and field equations for general relativity coupled to a Seiberg-Witten electromagnetic field. Noncommutativity enters the spacetime metric through a conformal factor and is responsible for dilating/contracting the separation between ...

Some consequences of promoting the object of noncommutativity theta(ij) to an operator in Hilbert space are explored. Its canonical conjugate momentum is also introduced. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which permits us to construct theories that are dynamically invariant under the action of the rotation group. In this framework ...

Noncommutative algebra in planar quantum mechanics is shown to follow from ’t Hooft’s recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a charged particle in a magnetic field with an oscillator potential are shown as dual descriptions of the same phenomenon. Finally, noncommutativity in a fluid dynamical model, analogous to the lowest ...

Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commut ative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its Weyl-Wigner deformed counterpart. In such representations, the effect of the noncommutativity on the bas...

We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N -soliton solution. For the example of the Moyal algebra, we find multi-soliton solutions for arbitrary space-space noncommutativity. The noncommutativity of coordinates is shown to obstruct the general construction of a τ function for these solitons. We investigate the two-soliton s...