We show that the large number coincidence can be interpreted as giving the filling factor in a Landau problem. The analogy with the Landau problem leads to noncommutativity between the gravitational and matter degrees of freedom. We present a toy model that supports this view. We present, also, some of the physical consequences this noncommutativity implies like a different insight into the sem...

We study the Connes spectral distance of quantum states and analyse nonlocality a 4D generalized noncommutative phase space. By virtue Hilbert–Schmidt operatorial formulation, we obtain Dirac operator construct triple corresponding to Based on ball condition, some constraint relations about optimal elements, then calculate between two Fock states. Due noncommutativity, distances in spaces are s...

We study dynamical effects of introducing noncommutativity on string worldsheets by using a matrix model obtained from the zero-volume limit of four-dimensional SU(N) Yang-Mills theory. Although the dimensionless noncommutativity parameter is of order 1/N , its effect is found to be non-negligible even in the large N limit due to the existence of higher Fourier modes. We find that the Poisson b...

Recently,in a paper hep-th/0511197, it was found that non-commutative super Yang-Mills (NCSYM) theory with space-dependent noncommutativity can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe supported by a flux of the NSNS B-field. Under S-duality, we show that this theory turns into a noncommutative open string (NCOS) theory with space-depend...

We investigate the condition for eternal inflation to take place in the noncommutative spacetime. We find that the possibility for eternal inflation’s happening is greatly suppressed in this case. If eternal inflation can not happen in the low energy region where the noncommutativity is very weak (the UV region), it will never happen along the whole inflationary history. Based on these conclusi...

The thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, the equations of state and thermodynamic response functions are explicitly given, and the effect of noncommutativity and quantum correction is discussed. It is shown that the well-known divergence exhibited in specific heat is ...

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 ...

The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic di-pole of a cold Rydberg atom is arranged in appropriate electric and magnetic fields, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads the canonical angular momentum to possess fractional values. In the limit of vanishing kinetic e...

Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative effects in a Gaussian wavepacket through the broadening of its width. We also rederive results on ∗-product of Gaussian wavepackets. In the second part, we constru...

We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures defined on the 4D (non-)commutative cotangent manifold. The noncommutativity exists in the coordinates or the momentum planes embedded in the 4D cotangent mani...