Noncommutative QED Research Articles

Perturbative quantization of two-dimensional space-time noncommutative QED

Using the method of perturbative quantization in the first order approximation, we quantize a non-local QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e^2,\theta^3), where e is the NC-QED coupling constant and \theta is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e^2,\theta^3. Using these commutation relations, the canonical current algebra of the modified theory is also derived.

Noncommutative GUT inspired theories with U(1) andSU(N)groups and their renormalizability

We consider the grand unified theory (GUT)-compatible formulation of noncommutative QED, as well as noncommutative $\mathrm{SU}(N)$ GUTs, for $N>2$, with no scalars but with fermionic matter in an arbitrary, anomaly-free representation, in the enveloping-algebra approach. We compute, to first order in the noncommutativity parameters ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}$, the UV divergent part of the one-loop background-field effective action involving at most two fermion fields and an arbitrary number of gauge fields. It turns out that, for special choices of the ambiguous trace over the gauge degrees of freedom, for which the $O(\ensuremath{\theta})$ triple gauge-field interactions vanish, the divergences can be absorbed by means of multiplicative renormalizations and the inclusion of $\ensuremath{\theta}$-dependent counterterms that vanish on shell and are thus unphysical. For this to happen in the $\mathrm{SU}(N)$, $N>2$ case, the representations of the matter fields must have a common second Casimir; anomaly cancellation then requires the ordinary (commutative) matter content to be nonchiral. Together with the vanishing of the divergences of fermionic four point functions, this shows that GUT-inspired theories with U(1) and $\mathrm{SU}(N)$, $N>2$ gauge groups and ordinary vector matter content not only have a renormalizable matter sector, but are on-shell one-loop multiplicatively renormalizable at order one in $\ensuremath{\theta}$.

QED ON THE GROENEWOLD–MOYAL PLANE

We investigate a version of noncommutative QED where the interaction term, although natural, breaks the spin-statistics connection. We calculate e- + e- → e- + e- and γ + e- → γ + e- cross-sections in the tree approximation and explicitly display their dependence on θμν. Remarkably the zero of the elastic e- + e- → e- + e- cross-section at 90° in the center-of-mass system, which is due to Pauli principle, is shifted away as a function of θμν and energy.

UV/IR mixing in noncommutative QED defined by Seiberg-Witten map

Noncommutative gauge theories defined via Seiberg-Witten map have desirable properties that theories defined directly in terms of noncommutative fields lack, covariance and unrestricted choice of gauge group and charge being among them, but nonperturbative results in the deformation parameter \theta are hard to obtain. In this article we use a \theta-exact approach to study UV/IR mixing in a noncommutative quantum electrodynamics (NCQED) model defined via Seiberg-Witten map. The fermion contribution of the one loop correction to the photon propagator is computed and it is found that it gives the same UV/IR mixing term as a NCQED model without Seiberg-Witten map.

Nilpotent noncommutativity and renormalization

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new four-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with a usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizability properties of NC theories.

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.

Recursive relations for processes with n photons of noncommutative QED

Recursion relations are derived in the sense of Berends–Giele for the multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level. It is shown that despite of the dependence of noncommutative vertices on momentum, in contrast to momentum-independent color factors of QCD, the recursion relation method can be employed for multi-photon processes of noncommutative QED.

Fermionic contributions to the free energy of noncommutative quantum electrodynamics at high temperature

We consider the fermionic contributions to the free energy of noncommutative QED at finite temperature T. This analysis extends the main results of our previous investigation where we have considered the pure bosonic sector of the theory. For large values of θT2 (θ is the magnitude of the noncommutative parameters) the fermionic contributions decrease the value of the critical temperature, above which there occurs a thermodynamic instability.

Light propagation in a background field for time–space non-commutativity and axionic non-commutative QED

We study the low-energy effects of space–time non-commutativity on light propagation in a background electromagnetic field. Contrary to some of the previous claims, we find no polarization rotation for vanishing time–space commutator [ x ˆ i , x ˆ 0 ] = 0 , although dispersion relation is modified, allowing for propagation faster than the vacuum speed of light. For non-zero [ x ˆ i , x ˆ 0 ] , as allowed with a proper quantization, a naive rotation effect is found to be actually absent when physical fields are defined through Seiberg–Witten map. We also consider non-commutative QED weakly coupled to small mass particles such as axions. Non-commutativity is found to dominate the inverse oscillation length, compared to axion mass and QED effects, for mixing particle masses smaller than 10 −12 eV . Conventional constraints on axion coupling based on photon–axion transition rates are unmodified, however induced ellipticity is proportional to the non-commutativity squared length scale. This last effect is found to be too small to account for the ellipticity reported by the PVLAS experiment, yet unexplained by conventional QED or axion physics.

Cancellation of soft and collinear divergences in noncommutative QED

In this paper, we investigate the behavior of noncommutative IR divergences and will also discuss their cancellation in the physical cross sections. The commutative IR (soft) divergences existing in the nonplanar diagrams will be examined in order to prove an all-order cancellation of these divergences using the Weinberg's method. In noncommutative QED, collinear divergences due to triple photon splitting vertex, were encountered, which are shown to be canceled out by the noncommutative version of KLN theorem. This guarantees that there is no mixing between the Collinear, soft divergences and noncommutative IR divergences.

ON THE ANOMALIES AND SCHWINGER TERMS IN NONCOMMUTATIVE GAUGE THEORIES

Invariant (nonplanar) anomaly of noncommutative QED is reexamined in this paper. It is found that just as in ordinary gauge theory UV regularization is needed to discover anomalies, in noncommutative case, in addition, an IR regularization is also required to exhibit the existence of invariant anomaly. Thus resolving the controversy in the value of invariant anomaly, an expression for the unintegrated anomaly is found. Schwinger terms of the current algebra of the theory are derived.

Unusual high-energy phenomenology of Lorentz-invariant noncommutative field theories

It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over these coordinates in the action produces a four-dimensional effective theory with Lorentz invariance intact. Previous applications of this approach, in particular to a specific construction of noncommutative QED, have been studied only in a low-momentum approximation. Here we discuss Lorentz-invariant field theories in which the relevant physics can be studied without requiring an expansion in the inverse scale of noncommutativity. Qualitatively, we find that tree-level scattering cross sections are dramatically suppressed as the center-of-mass energy exceeds the scale of noncommutativity, that cross sections that are isotropic in the commutative limit can develop a pronounced angular dependence, and that nonrelativistic potentials (for example, the Coloumb potential) become nonsingular at the origin. We consider a number of processes in noncommutative QED that may be studied at a future linear collider. We also give an example of scattering via a four-fermion operator in which the noncommutative modifications of the interaction can unitarize the tree-level amplitude, without requiring any other new physics in the ultraviolet.

Gauge-invariant resummation formalism and unitarity in non-commutative QED

We re-examine the perturbative properties of four-dimensional non-commutative QED by extending the pinch techniques to the theta-deformed case. The explicit independence of the pinched gluon self-energy from gauge-fixing parameters, and the absence of unphysical thresholds in the resummed propagators permits a complete check of the optical theorem for the off-shell two-point function. The known anomalous (tachyonic) dispersion relations are recovered within this framework, as well as their improved version in the (softly broken) SUSY case. These applications should be considered as a first step in constructing gauge-invariant truncations of the Schwinger-Dyson equations in the non-commutative case. An interesting result of our formalism appears when considering the theory in two dimensions: we observe a finite gauge-invariant contribution to the photon mass because of a novel incarnation of IR/UV mixing, which survives the commutative limit when matter is present.

Nondecoupling phenomena in QED in a magnetic field and noncommutative QED

The dynamics in QED in a strong constant magnetic field and its connection with the noncommutative QED are studied. It is shown that in the regime with the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion determinant is transformed into the noncommutative U(1)nc gauge symmetry. In this regime, the effective action is intimately connected with that in noncommutative QED and the original U(1) gauge Ward identities are broken (the LLL anomaly). On the other hand, it is shown that although a contribution of each of an infinite number of higher Landau levels is suppressed in an infrared region, their cumulative contribution is not (a nondecoupling phenomenon). This leads to a restoration of the original U(1) gauge symmetry in the infrared dynamics. The physics underlying this phenomenon reflects the important role of a boundary dynamics at spatial infinity in this problem.

Photon deflection by a Coulomb field in noncommutative QED

In noncommutative QED photons present self-interactions in the form of triple and quartic interactions. The triple interaction implies that, even though the photon is electrically neutral, it will deflect when in the presence of an electromagnetic field. If detected, such deflection would be undoubted evidence of noncommutative space-time. In this work we derive a general expression for the deflection of a photon by any electromagnetic field. As an application we consider the case of the deflection of a photon by an external static Coulomb field.

MATRIX MODELS OF NONCOMMUTATIVE 3D LATTICE GAUGE THEORIES

We investigate through the Morita equivalence the problem of mapping, odd dimensional noncommutative lattice gauge theories onto suitable matrix models. We specialize our analysis to three-dimensional noncommutative QED (NCQED) and scalar QED (NCsQED), for which we explicitly build the corresponding matrix model.

Parton model in Lorentz invariant noncommutative space

We consider the Lorentz invariant non-commutative QED and complete the Feynman rules for the theory up to the order $\theta^2$. In the Lorentz invariant version of the non-commutative QED the particles with fractional charges can be also considered. We show that in the parton model, even at the lowest order, the Bjorken scaling violates as $\sim\theta^2Q^4$.

Testing non-commutative QED $\gamma\gamma\gamma$ and $\gamma\gamma\gamma\gamma$ couplings at LHC

In this work, we investigate the sensitivity of the process p + p --> q + q --> j + j + gamma + gamma at LHC for the photonic 3- and 4- point functions that appear in non commutative QED. We show that this process serves to study the behavior of the space-space as well as of the space-time non commutativity. We also show that this process can probe the non commutative scale in the range of few TeV.

On the classical dynamics of charges in non-commutative QED

Following Wong’s approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space.

Test of non-commutative QED at LEP

Abstract If the space-time coordinates are actually non-commutative, the quantum field theory will have to be modified. Non-commutative QED, an example of such theory, involves violation of Lorenz nvariance and predicts deviations from the Standard Model depending on the new energy scale ΛNC and on unique directions in space. A study is made using the high energy e+e−1 collision data at LEP.