Covariant Quantum Fields on Noncommutative Spacetimes

A spinless covariant field $\phi$ on Minkowski spacetime \M^{d+1} obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group \Pg and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for Moyal spacetimes are derived transparently. For the Voros algebra, covariance and the *-operation are in conflict so that there are no covariant Voros fields compatible with *, a result we found earlier. The notion of Drinfel'd twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons. For twists involving nonabelian groups the emergent spacetimes are nonassociative.Comment: 20 page

Quantum Geons and Noncommutative Spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group $S_N$. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the commutative spacetime algebras of geons as well to noncommutative algebras. The latter support twisted actions of diffeos of geon spacetimes and associated twisted statistics. The notion of covariant fields for geons is formulated and their twisted versions are constructed from their untwisted versions. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli principle, seem to be the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.Comment: 41 page

Non-Linear Sigma Model on the Fuzzy Supersphere

In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S^(2,2). In hep-th/0212133 Bott projectors have been used to obtain the fuzzy CP^1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super) -projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model.Comment: 11 pages, LaTeX, corrected typo

Topology in Physics - A Perspective

This article, written in honor of Fritz Rohrlich, briefly surveys the role of topology in physics.Comment: 16pp, 2 figures included (encapsulated postscript

Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics

Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility arises for example in theories with a compact extra dimension with which time does not commute. The above results suggest striking phenomenological consequences in extra dimensional theories and elsewhere. In this paper we develop scattering theory for discrete time translations. It enables the calculation of transition probabilities for energy nonconserving processes and has a central role both in formal theory and phenomenology. We can also consider space-space noncommutativity where one of the spatial directions is a circle. That leads to the quantisation of the remaining spatial direction and conservation of momentum in that direction only modulo some fixed unit, as a simple adaptation of the results in this paper shows.Comment: 17 pages, LaTex; minor correction

Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator

It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain an edge effect which corresponds precisely to the ``fuzzy'' $U(1)_A$ axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant expansion of the quark propagator in the form $\frac{1}{{\cal D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}}$ where $a=\frac{2}{2l+1}$ is the lattice spacing on ${\bf S}^2_F$, $\hat{\Gamma}^L$ is the covariant noncommutative chirality and ${\cal D}_{Aa}$ is an effective Dirac operator which has essentially the same IR spectrum as ${\cal D}_{AF}$ but differes from it on the UV modes. Most remarkably is the fact that both operators share the same limit and thus the above covariant expansion is not available in the continuum theory . The first bit in this expansion $\frac{a\hat{\Gamma}^L}{2}$ although it vanishes as it stands in the continuum limit, its contribution to the anomaly is exactly the canonical theta term. The contribution of the propagator $\frac{1}{{\cal D}_{Aa}}$ is on the other hand equal to the toplogical Chern-Simons action which in two dimensions vanishes identically .Comment: 26 pages, latex fil

Mobile robot based electrostatic spray system for controlling pests on cotton plants in Iraq

A mobile robot based electrostatic spray system was developed to combat pest infestation on cotton plants in Iraq. The system consists of a charged spray nozzle, a CCD camera, a mobile robot (vehicle and arm) and Arduino microcontroller. Arduino microcontroller is used to control the spray nozzle and the robot. Matlab is used to process the image from the CCD camera and to generate the appropriate control signals to the robot and the spray nozzle. COMSOL multi-physics FEM software was used to design the induction electrodes to achieve maximum charge transfer onto the fan spray liquid film resulting in achieving the desired charge/mass ratio of the spray. The charged spray nozzle was operated on short duration pulsed spray mode. Image analysis was employed to investigate the spray deposition on improvised insect targets on an artificial plant.The ministry of higher education and scientific research of Iraqi governmen

The Fermion Doubling Problem and Noncommutative Geometry

We propose a resolution for the fermion doubling problem in discrete field theories based on the fuzzy sphere and its Cartesian products.Comment: 12 pages Latex2e, no figures, typo

Frequency-sweep examination for wave mode identification in multimodal ultrasonic guided wave signal

This article has been made available through the Brunel Open Access Publishing Fund.Ultrasonic guided waves can be used to assess and monitor long elements of a structure from a single position. The greatest challenges for any guided wave system are the plethora of wave modes arising from the geometry of the structural element which propagate with a range of frequency-dependent velocities and the interpretation of these combined signals reflected by discontinuities in the structural element. In this paper, a novel signal processing technique is presented using a combination of frequency-sweep measurement, sampling rate conversion, and Fourier transform. The technique is applied to synthesized and experimental data to identify different modes in complex ultrasonic guided wave signals. It is demonstrated throughout the paper that the technique also has the capability to derive the time of flight and group velocity dispersion curve of different wave modes in field inspections. © 2014 IEEE

Scalar Field Theory on Fuzzy S^4

Scalar fields are studied on fuzzy $S^4$ and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4 in the fuzzy context.Comment: 16 pages, LaTe