Noncommutativity of space coordinates has been much studied from various points of view [1-3]. It arises naturally in string theory, where it is related to the presence of strong backgrounds fields. If these are constant, one obtains the more familiar case where the coordinate noncommutativity [x, x ] is a constant antisymmetric quantity. However, if the background fields depend on the spatial ...

We study the noncommutative inflation with a time-dependent noncommutativity between space and time. From the numerical analysis of power law inflation, there are clues that the CMB spectrum indicates a nonconstant noncommutative inflation. Then we extend our treatment to the inflation models with more general noncommutativity and find that the scalar perturbation power spectrum depends sensiti...

We elucidate the connection between the N = 1 β–deformed SYM theory and noncommutativity. Our starting point is the T–duality generating transformation involved in constructing the gravity duals of both β–deformed and noncommutative gauge theories. We show that the two methods can be identified provided that a particular submatrix of the O(3, 3,R) group element employed in the former case, is i...

Abstract Coordinate noncommutativity, rather than being introduced through deformations of operator products, is achieved by coupling an auxiliary system with large energy excitations to the one of interest. Integrating out the auxiliary dynamics, or equivalently taking ground state expectation values, leads to the desired coordinate noncommutativity. The product responsible for this noncommuta...

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 manifolds. The noncommutativity exists equivalently in the coordinate or the momentum planes embedded in the 4D c...

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 manifolds. The noncommutativity exists equivalently in the coordinate or the momentum planes embedded in the 4D c...

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 manifolds. The noncommutativity exists equivalently in the coordinate or the momentum planes embedded in the 4D c...