We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. The...

Non-Commutative (NC) effects in planar quantum mechanics are investigated. We have constructed a Master model for a noncommutative harmonic oscillator by embedding it in an extended space, following the Batalin-Tyutin [5] prescription. Different gauge choices lead to distinct NC structures, such as NC coordinates, NC momenta or noncommutativity of a more general kind. In the present framework, ...

We consider Feynman’s path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their co...

Upon applying Chamseddine’s noncommutative deformation of gravity we obtain the leading order noncommutative corrections to the Robertson-Walker metric tensor. We get an isotropic inhomogeneous metric tensor for a certain choice of the noncommutativity parameters. Moreover, the singularity of the commutative metric at t = 0 is replaced by a more involved space-time structure in the noncommutati...

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On...

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either c...

One presents a phase-space noncommutative extension of Quantum Cosmology in the context of a Kantowski-Sachs (KS) minisuperspace model. We obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten map. The resulting WDW equation explicitly depends on the phase-space noncommutative parameters, θ and η. Numerical solutions of th...

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either c...

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative φ⋆4 scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative...

We demonstrate the existence of entanglement in a system harmonic oscillators placed noncommutative plane (“exotic oscillators”) by computing entropy as measured von Neumann reduced density matrix. It is explicitly verified that arises from noncommutativity, which controls coupling strength between spatial modes. This can easily be generalized to case where momentum components also satisfy rela...