Narrow Results

In this paper, we investigate the thermodynamic properties of the Schwarzschild–Tangherlini black hole in $D$-dimension in a generic noncommutativity setting in which geometry and matter are affected. A mass density and radial coordinate ($r$) are used to carry out this assignment. At this point, the transition on the radial coordinate $r$ is really performed in the same space contrary to the Bopp shift, which requires us to operate in phase space. By contrasting our model with that of earlier research on noncommutative inspired geometry, we are able to see how two-fold deformation affects our black hole’s thermodynamic characteristics.

In this paper we study the effects of noncommutativity on a closed superstring propagating in the space–time that is compactified on tori. The effects of compactification and noncommutativity appear in the momentum, quantization, supercurrent, super-conformal generators and in the boundary state of the closed superstring emitted from a D_p-brane with the NS ⊗ NS background B-field.

Using the notions of gauge symmetry and gauge connection on ordinary superspaces, we derive a class of generalized supertranslation algebras in the case of N = 1, D = 2 Euclidean superspace with a U(1) gauge group. This generalizes the ordinary algebra by inclusion of some additional bosonic and fermionic operators which are interpreted as the generators of the U(1) gauge symmetry on superspace. The generalized superalgebra closes only for very particular configurations of the gauge connection superfield. This provides a unified framework for a variety of generalizations of the ordinary superalgebra such as its central extension and its noncommutative deformation found in an earlier work.

In this paper we study the noncommutativity of a moving membrane with background fields. The open string variables are analyzed. Some scaling limits are studied. The equivalence of the magnetic and electric noncommutativities is investigated. The conditions for equivalence of noncommutativity of the T-dual theory in the rest frame and noncommutativity of the original theory in the moving frame are obtained.

In this paper we consider an open string attached to a Dp-brane, in the presence of the pp-wave and background gauge fields. The effects of the string mass on the open string propagator, open string metric and the noncommutativity parameter are studied. Some free matrices appear in the propagator and in the open string variables. The symmetries of the string propagator and consistency with the zero mass case put some restrictions on these matrices.

In this paper, we present a general modified dispersion relation derived from q-deformed noncommutative theory and apply it to the ultrahigh energy cosmic ray and the TeV-photon paradoxes — threshold anomalies. Our purpose is not only trying to solve these puzzles by noncommutative theory but also to support noncommutative theory through the coincidence of the region in the parameter space for resolving the threshold anomalies with the one from the q-deformed noncommutative theory.

In this paper some properties of the superstring with noncommutative worldsheet are studied. We study the noncommutativity of the spacetime, generalization of the Poincaré symmetry of the superstring, the changes of the metric, antisymmetric tensor and dilaton.

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a Gödel-type metric.

We study how the noncommutative spacetime affects inflation. First we obtain the noncommutative power spectrum of the curvature perturbations produced during inflation in the slow-roll approximation. This is the explicit k-dependent power spectrum up to first order in slow-roll parameters ε₁, δ₁ including the noncommutative parameter μ. In order to test the role of μ further, we calculate the noncommutative power spectrum using the slow-roll expansion. We find corrections which arise from the change of pivot scale and the slowly varying nature of μ. It turns out that the noncommutative parameter μ could be considered as a zero order slow-roll parameter and the noncommutative spacetime effect provides a negatively large running spectral index.

We consider the generic non-anticommutative model of chiral–antichiral superfields on superspace. The model is formulated in terms of an arbitrary Kählerian potential, chiral and antichiral superpotentials and can include the non-anticommutative supersymmetric sigma-model as a partial case. We study a component structure of the model and derive the component Lagrangian in an explicit form with all auxiliary fields contributions. We show that the infinite series in the classical action for generic non-anticommutative model of chiral–antichiral superfields in D = 4 dimensions can be resumed in a compact expression which can be written as a deformation of standard Zumino's Lagrangian and chiral superpotential. Problem of eliminating the auxiliary fields in the generic model is discussed and the first perturbative correction to the effective scalar potential is obtained.

A novel approach to the analysis of a noncommutative Chern–Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg–Witten map which is exact in the noncommutative parameter.

The Maxwell–Chern–Simons model with scalar matter in the adjoint representation is analyzed from an alternative approach which is regular in the θ→0 limit. This method is complementary to the usual operator formalism applied to explore the nonperturbative solutions which give singular results in the θ→0 limit. The absence of any regular non-trivial lumpy solutions satisfying B–P–S bound has been conclusively demonstrated.

The (1+1)-dimensional bosonized Schwinger model with a generalized gauge-invariant regularization has been studied in a noncommutative scenario. The original commutative model with the indicated regularization revealed the transition from confinement to deconfinement of the fermion.¹⁰ We show that though the introduction of spacetime noncommutativity gives rise to new features in the confinement scenario, it does not affect the deconfining limit.

We investigate the physical implications of the noncommutative geometry in inflationary scenario. Firstly we study the noncommutative inflation with a time-dependent noncommutativity between space and time and find that the scalar perturbation power spectrum depends sensitively on the time varying of the spacetime noncommutativity. Secondly, we discuss the spatially noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of noncommutativity and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. It turns out that the corrections are sensitive to the speed of sound and the choice of string length scale, and the shapes of the corrected non-Gaussianities are distinct from that of ordinary ones.

Generally, in the presence of an antisymmetric tensor background field, the open string moving with mixed Neumann and Dirichlet boundary conditions will make the spacetime coordinates noncommutative. In this paper, comparing to the flat and static D-brane case studied in the literature, we first generalize the D-branes to be dynamical. And then by using the Hamiltonian approach, through a calculation of the classical Poisson brackets among the Fourier mode components of the string embedding coordinates and a consistent quantization procedure, we show that the spacetime coordinates of the string endpoints in the directions parallel and perpendicular to the D-branes both become noncommutative.

The open string ending on a flat D-brane in the pp-wave background with a constant B-field is exactly solvable but will be controlled by a more mass parameter. In this paper we mainly quantize this open string theory canonically by employing the Faddeev–Jackiw symplectic quantization procedure, and find that the phase space of the string coordinate and canonical momentum becomes fully noncummutative, consistent with the results obtained previously.

In this letter we study the effects of a noncommutative minisuperspace, including matter degrees of freedom on a toy model for FRW universe with cosmological constant. In this simple model the vacuum energy density is modified by the presence of the noncommutative minisuperspace parameter, from which we conjecture on the discrepancy between the calculated and observed vacuum energy density associated to Λ.

In this paper, the microcausality of quantum field theory on spin-induced noncommutative spacetime is discussed. It is found that for space-like separation the microcausality is not obeyed by the theory generally. It means that Lorentz covariance cannot guarantee microcausality in quantum field theory. We also give some comments about quantum field theories on such noncommutative spacetime and the relations between noncommutative spacetime and causality.

Using noncommutative infinitesimal rotations, we work out a formulation for angular momentum which leads to an expression for nuclear magnetic resonance (NMR). We also indicate a cosmic footprint of these considerations, much like the 21 cm radio signal of cosmic Hydrogen. Here, the motivation is that there are a number of “second-order effects” which provide results over and above the usual well-known results.

The present work investigates the implications of incorporating noncommutativity into $f(R)$ gravity. In particular, we explore the proposed framework in a flat Friedmann–Robertson–Lamaître–Walker background. We introduced the noncommutativity between the coordinates and the momenta, in a $2n$-dimensional phase space. Applying the machinery of canonical quantization we obtain the noncommutative version of the Wheeler–DeWitt equation, and using a WKB-type approximation we can get analytical solutions for the model examining two cases for the leading noncommutative coefficient. In the first, solutions for the scale factor present a structure similar to previous solutions reported in the literature. The second one, in contrast to its commutative counterpart, the solutions obtained for the scale factor show that its evolution has the behavior of a non-singular cyclic universe. Also, we present the demeanor of the Hubble parameter and the effective equation of state parameter, where the latter crosses the “$-1$” divide line.