Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing

We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the phase appearing in the nonplanar diagrams is the one given by the commutator of the coordinates, the semiclassical Poisson structure of the non commutative spacetime. We do this with an explicit calculation for represented generic products.Comment: 24 pages, 1 figur

Renormalisation of \phi^4-theory on noncommutative R^2 in the matrix base

As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is renormalisable in momentum space arguing that there would be logarithmic UV/IR-divergences only. Although momentum space Feynman graphs can indeed be computed to any loop order, the logarithmic UV/IR-divergence appears in the renormalised two-point function -- a hint that the renormalisation is not completed. In particular, it is impossible to define the squared mass as the value of the two-point function at vanishing momentum. In contrast, in our matrix approach the renormalised N-point functions are bounded everywhere and nevertheless rely on adjusting the mass only. We achieve this by introducing into the cut-off model a translation-invariance breaking regulator which is scaled to zero with the removal of the cut-off. The naive treatment without regulator would not lead to a renormalised theory.Comment: 26 pages, 44 figures, LaTe

Star Product and Invariant Integration for Lie type Noncommutative Spacetimes

We present a star product for noncommutative spaces of Lie type, including the so called ``canonical'' case by introducing a central generator, which is compatible with translations and admits a simple, manageable definition of an invariant integral. A quasi-cyclicity property for the latter is shown to hold, which reduces to exact cyclicity when the adjoint representation of the underlying Lie algebra is traceless. Several explicit examples illuminate the formalism, dealing with kappa-Minkowski spacetime and the Heisenberg algebra (``canonical'' noncommutative 2-plane).Comment: 21 page

Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly1

Configuration (x-)space renormalization of euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group

Degenerate noncommutativity

We study a renormalizable four dimensional model with two deformed quantized space directions. A one-loop renormalization is performed explicitly. The Euclidean model is connected to the Minkowski version via an analytic continuation. At a special value of the parameters a nontrivial fixed point of the renormalization group occurs.Comment: 16 page

Pair Production of Neutral Higgs Bosons through Noncommutative QED Interactions at Linear Colliders

We study the feasibility of detecting noncommutative (NC) QED through neutral Higgs boson (H) pair production at linear colliders (LC). This is based on the assumption that H interacts directly with photon in NCQED as suggested by symmetry considerations and strongly hinted by our previous study on \pi^0-photon interactions. We find the following striking features as compared to the standard model (SM) result: (1) generally larger cross sections for an NC scale of order 1 TeV; (2) completely different dependence on initial beam polarizations; (3) distinct distributions in the polar and azimuthal angles; and (4) day-night asymmetry due to the Earth's rotation. These will help to separate NC signals from those in the SM or other new physics at LC. We emphasize the importance of treating properly the Lorentz noninvariance problem and show how the impact of the Earth's rotation can be used as an advantage for our purpose of searching for NC signals.Comment: 12 pages, 3 figures using axodraw.sty; v2: proof version in Phys. Rev. D, minor rewordin

Anomaly freedom in Seiberg-Witten noncommutative gauge theories

We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the \epsilon^{\m_1\m_2\m_3\m_4} part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter \theta^{\m\n}. And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.Comment: LaTeX 2e, no macros, no figures, 32 A4 page

Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which based on Weyl symmetrically ordered operator products. By using a polydifferential representation for deformed coordinates $\hat x^j$ we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.Comment: 20 pages, v2, v3: comments and references adde