Noncommutative Parameter Research Articles

On the deformed squeezed states on noncommutative plane

Abstract A new kind of deformed boson operators is proposed to be consistent with the large noncommutativity parameters on noncommutative plane when noncommutativity of momentum spaces is considered. Using this kind of deformed boson operators, the coherent states and squeezed states are constructed, and their properties are discussed in detail.

FermionicTduality and momenta noncommutativity

In this article we establish the relationship between fermionic T-duality and momenta noncommuativity. This is extension of known relation between bosonic T-duality and coordinate noncommutativity. The case of open string propagating in background of the type IIB superstring theory has been considered. We perform T-duality with respect to the fermionic variables instead to the bosonic ones. We also choose Dirichlet boundary conditions at the string endpoints, which lead to the momenta noncommutativity, instead Neumann ones which lead to the coordinates noncommutativity. Finally, we establish the main result of the article that momenta noncommutativity parameters are just fermionic T-dual fields.

Classical noncommutative electrodynamics with external source

In a $U(1)_{\star}$-noncommutative (NC) gauge field theory we extend the Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external current and formulate - to the first order in the NC parameter - gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size $a$, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, $1/r$ included, from the solutions. The static charge proves to be a magnetic dipole, with its magnetic moment being inversely proportional to its size $a$. The external magnetic field modifies the long-range Coulomb field and some electromagnetic form-factors. We also analyze the ambiguity in the SW map and show that at least to the order studied here it is equivalent to the ambiguity of adding a homogeneous solution to the current-conservation equation.

Chiral symmetry restoration in holographic noncommutative QCD

We consider the noncommutative deformation of the Sakai--Sugimoto model at finite temperature and finite baryon chemical potential. The space noncommutativity is possible to have an influence on the flavor dynamics of the QCD. The critical temperature and critical value of the chemical potential are modified by the space noncommutativity. The influence of the space noncommutativity on the flavor dynamics of the QCD is caused by the Wess--Zumino term in the effective action of the D8-branes. The intermediate temperature phase, in which the gluons deconfine but the chiral symmetry remains broken, is easy to be realized in some region of the noncommutativity parameter.

Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

We calculate the Komar energy $E$ for a noncommutative Schwarzschild black hole. A deformation from the conventional identity $E=2ST_H$ is found in the next to leading order computation in the noncommutative parameter $\theta$ (i.e. $\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})$) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result $M=2ST_H$, where the mass ($M$) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter--Schwarzschild geometry.

Higgs-strahlung and pair production in thee+e−collision in the noncommutative standard model

The higgsstrahlung process $e^+e^-\to Z H$ and pair production process $e^+e^- \to H H$ are studied in the framework of the minimal noncommutative (NC) standard model. In particular, the Feynman rules involving all orders of the noncommutative parameter $\theta$ are derived using reclusive formation of Seiberg-Witten map. It is shown that the total cross section and angular distribution can be significantly affected because of spacetime noncommutativity when the collision energy exceeds to 1 \tev. It is found that in each process, there is an optimal collision energy ($E_{oc}$) for achieving the greatest noncommutative effect, and $E_{oc}$ varies linearly with the NC scale $\Lambda_{NC}$. A brief discussion on the process $e^+e^- \to\mu^+ \mu^-$ is also given.

Gluon scattering amplitudes in finite temperature gauge/gravity dualities

We examine the gluon scattering amplitude in \( \mathcal{N} = 4 \) super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wilson loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.

Non-commutativity parameters depend not only on the effective coordinate but on its T-dual as well

We extend our investigations of the open string propagation in the weakly curved background to the case when Kalb-Ramond field, beside the infinitesimal term linear in coordinate B μνρ x ρ, contains the constant term b μν ≠ 0. In two previously investigated cases, for the flat background (b μν ≠ 0 and B μνρ = 0) and the weakly curved one (b μν ≠ 0 and B μνρ = 0) the effective metric is constant and the effective Kalb-Ramond field is zero. In the present article (b μν ≠ 0 and B μνρ = 0) the effective metric is coordinate dependent and there exists non-trivial effective Kalb-Ramond field. It depends on the σ-integral of the effective momentum P μ(σ) = ∫ σ0 dηp μ(η), which is in fact T-dual of the effective coordinate, \( {P_\mu } = \kappa {g_{\mu \nu }}{\tilde{q}^\nu } \). Beside the standard coordinate dependent term θ μν(q), in the non-commutativity parameter, which is nontrivial only on the string end-points, there are additional P μ (or \( {\tilde{q}^\mu } \)) dependent terms which are nontrivial both at the string endpoints and at the string interior. The additional terms are infinitesimally small. The part of one of these terms has been obtained in ref. [22] and the others are our improvements.

Spin Hall effect on a noncommutative space

We study the spin-orbital interaction and the spin Hall effect(SHE) of an electron moving on a noncommutative space under the influence of a vector potential A. On a noncommutative space we find that the commutator between the vector potential A and the electric potential V_1(r) of lattice induces a new term which can be treated as an effective electric field, and the spin-Hall conductivity obtains some correction. In addition, the spin current as well as spin-Hall conductivity have distinct values in different direction. On a noncommutative space we derive the spin-depended electric current whose expectation value gives the spin Hall effect and spin Hall conductivity. We have defined a new parameter \varsigma=\rho\theta (\rho is electron concentration, \theta is noncommutative parameter) which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation which give a general Hamiltonian of a non-relativistic electron moving on a noncommutative space.

TeV scale implications of non commutative space time in laboratory frame with polarized beams

We analyze $e^{+}e^{-}\rightarrow \gamma\gamma$, $e^{-}\gamma \rightarrow e^{-}\gamma$ and $\gamma\gamma \rightarrow e^{+}e^{-} $ processes within the Seiberg-Witten expanded noncommutative scenario using polarized beams. With unpolarized beams the leading order effects of non commutativity starts from second order in non commutative(NC) parameter i.e. $O(\Theta^2)$, while with polarized beams these corrections appear at first order ($O(\Theta)$) in cross section. The corrections in Compton case can probe the magnetic component($\vec{\Theta}_B$) while in Pair production and Pair annihilation probe the electric component($\vec{\Theta}_E$) of NC parameter. We include the effects of earth rotation in our analysis. This study is done by investigating the effects of non commutativity on different time averaged cross section observables. The results which also depends on the position of the collider, can provide clear and distinct signatures of the model testable at the International Linear Collider(ILC).

Entropic gravity, phase-space noncommutativity and the equivalence principle

We generalize E Verlinde's entropic gravity reasoning to a phase-space noncommutativity setup. This allows us to impose a bound on the product of the noncommutative parameters based on the equivalence principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.

2+1 Dimensional Noncommutative Dirac Oscillator and (Anti)-Jaynes-Cummings Models

We study Dirac oscillator in 2+1 dimensional noncommutative space. The model is solved exactly and the relationship with Jaynes-Cummings (JC) or anti-Jaynes-Cummings (AJC) models are investigated. We find that for a positive noncommutative parameter, there is an exact map from the 2+1 dimensional noncommutative Dirac oscillator to AJC model. However, for a negative noncommutative parameter, the noncommutative planar Dirac oscillator contains both AJC and JC terms simultaneously. Our investigation may afford a new way to study relativistic quantum mechanics models in noncommutative space by means of quantum optics method, and vice verse.

Noncommutativity and Lorentz violation in relativistic heavy ion collisions

The experimental detection of the effects of noncommuting coordinates in electrodynamic phenomena depends on the magnitude of |\theta B|, where \theta is the noncommutativity parameter and B a background magnetic field. With the present upper bound on \theta, given by \theta_{\rm bound} \simeq 1/(10 {\rm TeV})^2, there was no large enough magnetic field in nature, including those observed in magnetars, that could give visible effects or, conversely, that could be used to further improve \theta_{\rm bound}. On the other hand, recently it has been proposed that intense enough magnetic fields should be produced at the beginning of relativistic heavy ion collisions. We discuss here lepton pair production by free photons as one kind of signature of noncommutativity and Lorentz violation that could occur at RHIC or LHC. This allows us to obtain a more stringent bound on \theta, given by 10^{-3} \theta_{\rm bound}, if such "exotic" events do not occur.

Classical mechanics on noncommutative space with Lie-algebraic structure

We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two new sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle interacting with a constant external force by means of the Hamiltonian formalism on a Poisson manifold. Our results not only include that of a recent work as our special cases, but also provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable t x ˙ - , ( xx ) ˙ -, and ( xx ) ¨ -dependence besides with the usual t-, x-, and x ˙ -dependence, originating from a variety of noncommutativity between different spatial coordinates and between spatial coordinates and momenta as well, deform greatly the particle’s ordinary trajectories we are quite familiar with on the Euclidean (commutative) space.

Magnetic monopole in noncommutative space-time and Wu-Yang singularity-free gauge transformations

We investigate the validity of the Dirac Quantization Condition (DQC) for magnetic monopoles in noncommutative space-time. We use an approach which is based on an extension of the method introduced by Wu and Yang. To study the effects of noncommutativity of space-time, we consider the gauge transformations of $U_\star(1)$ gauge fields and use the corresponding deformed Maxwell's equations. Using a perturbation expansion in the noncommutativity parameter $\theta$, we show that the DQC remains unmodified up to the first order in the expansion parameter. The result is obtained for a class of noncommutative source terms, which reduce to the Dirac delta function in the commutative limit.

Strong gravitational lensing in a noncommutative black-hole spacetime

Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Comparing to the Reissner-Norstr\"{om} black hole, we find that the influences of the spacetime noncommutative parameter is similar to those of the charge, just these influences are much smaller. This may offer a way to distinguish a noncommutative black hole from a Reissner-Norstr\"{om} black hole, and may probe the spacetime noncommutative constant $\vartheta$ \cite{foot} by the astronomical instruments in the future.

Noncommutativity in weakly curved background by canonical methods

Using the canonical method, we investigate the Dp-brane world-volume noncommutativity in a weakly curved background. The term ``weakly curved'' means that, in the leading order, the source of nonflatness is an infinitesimally small Kalb-Ramond field ${B}_{\ensuremath{\mu}\ensuremath{\nu}}$, linear in coordinate, while the Ricci tensor does not contribute, being an infinitesimal of the second order. On the solution of boundary conditions, we find a simple expression for the space-time coordinates in terms of the effective coordinates and momenta. This basic relation helped us to prove that noncommutativity appears only on the world sheet boundary. The noncommutativity parameter has a standard form, but with the infinitesimally small and coordinate-dependent antisymmetric tensor ${B}_{\ensuremath{\mu}\ensuremath{\nu}}$. This result coincides with that obtained on the group manifolds in the limit of the large level $n$ of the current algebra. After quantization, the algebra of the functions on the Dp-brane world volume is represented with the Kontsevich star product instead of the Moyal one in the flat background.

Neutral Higgs boson pair production at the linear collider in the noncommutative standard model

We study the Higgs boson pair production at the linear collider in the noncommutative extension of the standard model using the Seiberg-Witten map of this to the first order of the noncommutative parameter ${\ensuremath{\Theta}}_{\ensuremath{\mu}\ensuremath{\nu}}$. Unlike the standard model (where the process is forbidden) here the Higgs boson pair directly interacts with the photon. We find that the pair production cross section can be quite significant for the noncommutative scale $\ensuremath{\Lambda}$ lying in the range 0.5 TeV to 1.0 TeV. Using the experimental (LEP 2, Tevatron, and global electroweak fit) bound on the Higgs mass, we obtain $626\text{ }\text{ }\mathrm{GeV}\ensuremath{\le}\ensuremath{\Lambda}\ensuremath{\le}974\text{ }\text{ }\mathrm{GeV}$.

Chiral fermions in noncommutative electrodynamics: Renormalizability and dispersion

We analyze quantization of noncommutative chiral electrodynamics in the enveloping algebra formalism in linear order in noncommutativity parameter $\theta$. Calculations show that divergences exist and cannot be removed by ordinary renormalization, however they can be removed by the Seiberg-Witten redefinition of fields. Performing the redefinitions explicitly, we obtain renormalizable lagrangian and discuss the influence of noncommutativity on field propagation. Noncommutativity affects the propagation of chiral fermions only: half of the fermionic modes become massive and birefringent.

On noncommutative minisuperspace and the Friedmann equations

In this Letter we present a noncommutative version of scalar field cosmology. We find the noncommutative Friedmann equations as well as the noncommutative Klein–Gordon equation, interestingly the noncommutative contributions are only present up to second order in the noncommutative parameter. Finally we conclude that if we want a noncommutative minisuperspace with a constant noncommutative parameter as viable phenomenological model, the noncommutative parameter has to be very small.