Non-renormalizability of noncommutative SU(2) gauge theory

We analyze the divergent part of the one-loop effective action for the noncommutative SU(2) gauge theory coupled to the fermions in the fundamental representation. We show that the divergencies in the 2-point and the 3-point functions in the $\theta$-linear order can be renormalized, while the divergence in the 4-point fermionic function cannot.Comment: 15 pages, results presented at ESI 2d dilaton gravity worksho

Renormalizability of noncommutative SU(N) gauge theory

We analyze the renormalizability properties of pure gauge noncommutative SU(N) theory in the $\theta$-expanded approach. We find that the theory is one-loop renormalizable to first order in $\theta$.Comment: 11 pages, minor changes, accepted for publication in JHE

The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model

We study the form factors appearing in the inclusive decay b -> s g^*, in the framework of the noncommutative standard model. Here g^* denotes the virtual gluon. We get additional structures and the corresponding form factors in the noncommutative geometry. We analyse the dependencies of the form factors to the parameter p\Theta k where p (k) are the four momenta of incoming (outgoing) b quark (virtual gluon g^*, \Theta is a parameter which measures the noncommutativity of the geometry. We see that the form factors are weaklyComment: 8 pages, 7 figure

The one-loop renormalization of the gauge sector in the noncommutative standard model

In this paper we construct a version of the standard model gauge sector on noncommutative space-time which is one-loop renormalizable to first order in the expansion in the noncommutativity parameter $\theta$. The one-loop renormalizability is obtained by the Seiberg-Witten redefinition of the noncommutative gauge potential for the model containing the usual six representations of matter fields of the first generation.Comment: 16 pages, 2 figure

Dirac quantization of noncommutative Abelian Proca field

Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant. Then, the system of second class constraints is quantized by introducing Dirac brackets in the reduced phase space.Comment: 12 pages, minor revisio

Kontsevich product and gauge invariance

We analyze the question of $U_{\star} (1)$ gauge invariance in a flat non-commutative space where the parameter of non-commutativity, $\theta^{\mu\nu} (x)$, is a local function satisfying Jacobi identity (and thereby leading to an associative Kontsevich product). We show that in this case, both gauge transformations as well as the definitions of covariant derivatives have to modify so as to have a gauge invariant action. We work out the gauge invariant actions for the matter fields in the fundamental and the adjoint representations up to order $\theta^{2}$ while we discuss the gauge invariant Maxwell theory up to order $\theta$. We show that despite the modifications in the gauge transformations, the covariant derivative and the field strength, Seiberg-Witten map continues to hold for this theory. In this theory, translations do not form a subgroup of the gauge transformations (unlike in the case when $\theta^{\mu\nu}$ is a constant) which is reflected in the stress tensor not being conserved.Comment: 7 page

Probing Noncommutative Space-Time in the Laboratory Frame

The phenomenological investigation of noncommutative space-time in the laboratory frame are presented. We formulate the apparent time variation of noncommutativity parameter $\theta_{\mu\nu}$ in the laboratory frame due to the earth's rotation. Furthermore, in the noncommutative QED, we discuss how to probe the electric-like component $\overrightarrow{\theta_{E}}=(\theta_{01},\theta_{02},\theta_{03})$ by the process $e^-e^+\to\gamma\gamma$ at future $e^-e^+$ linear collider. We may determine the magnitude and the direction of $\overrightarrow{\theta_{E}}$ by detailed study of the apparent time variation of total cross section. In case of us observing no signal, the upper limit on the magnitude of $\overrightarrow{\theta_E^{}}$ can be determined independently of its direction.Comment: 12 pages, 7 figures, typos are corrected, one graph have been added in figure

π+π+\pi^+\pi^+ and π+π−\pi^+\pi^- colliding in noncommutative space

By studying the scattering process of scalar particle pion on the noncommutative scalar quantum electrodynamics, the non-commutative amendment of differential scattering cross-section is found, which is dependent of polar-angle and the results are significantly different from that in the commutative scalar quantum electrodynamics, particularly when $\cos\theta\sim \pm 1$. The non-commutativity of space is expected to be explored at around $\Lambda_{NC}\sim$TeV.Comment: Latex, 12 page

Towards Noncommutative Fuzzy QED

We study in one-loop perturbation theory noncommutative fuzzy quenched QED_4. We write down the effective action on fuzzy S**2 x S**2 and show the existence of a gauge-invariant UV-IR mixing in the model in the large N planar limit. We also give a derivation of the beta function and comment on the limit of large mass of the normal scalar fields. We also discuss topology change in this 4 fuzzy dimensions arising from the interaction of fields (matrices) with spacetime through its noncommutativity.Comment: 33 page

Signals for Non-Commutative QED in eγe \gamma and γγ\gamma \gamma Collisions

We study the effects of non-commutative QED (NCQED) in fermion pair production, gamma + gamma -> f + bar{f} and Compton scattering, e + gamma -> e + gamma. Non-commutative geometries appear naturally in the context of string/M-theory and gives rise to 3- and 4-point photon vertices and to momentum dependent phase factors in QED vertices which will have observable effects in high energy collisions. We consider e+ e- colliders with energies appropriate to the TeV Linear Collider proposals and the multi-TeV CLIC project operating in gamma gamma and e gamma modes. Non-commutative scales roughly equal to the center of mass energy of the e+ e- collider can be probed, with the exact value depending on the model parameters and experimental factors. However, we found that the Compton process is sensitive to Lambda_{NC} values roughly twice as large as those accessible to the pair production process.Comment: 24 pages, 11 eps figure files, RevTeX forma