Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the $\star$-product among the fields, compatible with the twisted Poincar\'e symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ($\theta_{0i}=0$), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.Comment: 16 pages, version to appear in J. Math. Phy

Noncommutativity and theta-locality

In this paper, we introduce the condition of theta-locality which can be used as a substitute for microcausality in quantum field theory on noncommutative spacetime. This condition is closely related to the asymptotic commutativity which was previously used in nonlocal QFT. Heuristically, it means that the commutator of observables behaves at large spacelike separation like $\exp(-|x-y|^2/\theta)$, where $\theta$ is the noncommutativity parameter. The rigorous formulation given in the paper implies averaging fields with suitable test functions. We define a test function space which most closely corresponds to the Moyal star product and prove that this space is a topological algebra under the star product. As an example, we consider the simplest normal ordered monomial $:\phi\star\phi:$ and show that it obeys the theta-locality condition.Comment: LaTeX, 17 pages, no figures; minor changes to agree with published versio

Cohomological Operators and Covariant Quantum Superalgebras

We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a unique superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GL_{qp} (1|1), is exactly identical to that obeyed by the de Rham cohomological operators. A set of discrete symmetry transformation for a set of GL_{qp} (1|1) covariant superalgebras turns out to be the analogue of the Hodge duality * operation of differential geometry. A connection with an extended BRST algebra obeyed by the nilpotent (anti-)BRST and (anti-)co-BRST charges, the ghost charge and a bosonic charge (which is equal to the anticommutator of (anti-)BRST and (anti-)co-BRST charges) is also established.Comment: LaTeX file, 21 page

Macrophage‐derived MMP‐9 enhances the progression of atherosclerotic lesions and vascular calcification in transgenic rabbits

Matrix metalloproteinase‐9 (MMP‐9), or gelatinase B, has been hypothesized to be involved in the progression of atherosclerosis. In the arterial wall, accumulated macrophages secrete considerable amounts of MMP‐9 but its pathophysiological functions in atherosclerosis have not been fully elucidated. To examine the hypothesis that macrophage‐derived MMP‐9 may affect atherosclerosis, we created MMP‐9 transgenic (Tg) rabbits to overexpress the rabbit MMP‐9 gene under the control of the scavenger receptor A enhancer/promoter and examined their susceptibility to cholesterol diet‐induced atherosclerosis. Tg rabbits along with non‐Tg rabbits were fed a cholesterol diet for 16 and 28 weeks, and their aortic and coronary atherosclerosis was compared. Gross aortic lesion areas were significantly increased in female Tg rabbits at 28 weeks; however, pathological examination revealed that all the lesions of Tg rabbits fed a cholesterol diet for either 16 or 28 weeks were characterized by increased monocyte/macrophage accumulation and prominent lipid core formation compared with those of non‐Tg rabbits. Macrophages isolated from Tg rabbits exhibited higher infiltrative activity towards a chemoattractant, MCP‐1 in vitro and augmented capability of hydrolysing extracellular matrix in granulomatous tissue. Surprisingly, the lesions of Tg rabbits showed more advanced lesions with remarkable calcification in both aortas and coronary arteries. In conclusion, macrophage‐derived MMP‐9 facilitates the infiltration of monocyte/macrophages into the lesions thereby enhancing the progression of atherosclerosis. Increased accumulation of lesional macrophages may promote vascular calcification.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154927/1/jcmm15087-sup-0001-FigS1-S13.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154927/2/jcmm15087.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154927/3/jcmm15087_am.pd

Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves

We characterize the worldvolume theories on symmetric D-branes in a six-dimensional Cahen-Wallach pp-wave supported by a constant Neveu-Schwarz three-form flux. We find a class of flat noncommutative euclidean D3-branes analogous to branes in a constant magnetic field, as well as curved noncommutative lorentzian D3-branes analogous to branes in an electric background. In the former case the noncommutative field theory on the branes is constructed from first principles, related to dynamics of fuzzy spheres in the worldvolumes, and used to analyse the flat space limits of the string theory. The worldvolume theories on all other symmetric branes in the background are local field theories. The physical origins of all these theories are described through the interplay between isometric embeddings of branes in the spacetime and the Penrose-Gueven limit of AdS3 x S3 with Neveu-Schwarz three-form flux. The noncommutative field theory of a non-symmetric spacetime-filling D-brane is also constructed, giving a spatially varying but time-independent noncommutativity analogous to that of the Dolan-Nappi model.Comment: 52 pages; v2: References adde

Gauge invariance and finite width effects in radiative two-pion tau lepton decay

The contribution of the rho^{\pm} vector meson to the tau -> pi pi nu gamma decay is considered as a potential source for the determination of the magnetic dipole moment of this light vector meson. In order to keep gauge-invariance of the whole decay amplitude, a procedure similar to the fermion loop-scheme for charged gauge bosons is implemented to incorporate the finite width effects of the rho^{\pm} vector meson. The absorptive pieces of the one-loop corrections to the propagators and electromagnetic vertices of the rho^{\pm} meson and W^{\pm} gauge boson have identical forms in the limit of massless particles in the loops, suggesting this to be a universal feature of spin-one unstable particles. Model-dependent contributions to the tau -> pi pi nu gamma decay are suppressed by fixing the two-pion invariant mass distribution at the rho meson mass value. The resulting photon energy and angular distribution is relatively sensitive to the effects of the rho magnetic dipole moment.Comment: 22 pages, 4 postscript figures, references and comments on relevance of perturbative treatment of rho electromagnetic vertex are added, accepted for pub. in Phys. Rev.

Advances in small lasers

M.T.H was supported by an Australian Research council Future Fellowship research grant for this work. M.C.G. is grateful to the Scottish Funding Council (via SUPA) for financial support.Small lasers have dimensions or modes sizes close to or smaller than the wavelength of emitted light. In recent years there has been significant progress towards reducing the size and improving the characteristics of these devices. This work has been led primarily by the innovative use of new materials and cavity designs. This Review summarizes some of the latest developments, particularly in metallic and plasmonic lasers, improvements in small dielectric lasers, and the emerging area of small bio-compatible or bio-derived lasers. We examine the different approaches employed to reduce size and how they result in significant differences in the final device, particularly between metal- and dielectric-cavity lasers. We also present potential applications for the various forms of small lasers, and indicate where further developments are required.PostprintPeer reviewe

Single amino acid substitutions in either YhjD or MsbA confer viability to 3-deoxy-d- manno -oct-2-ulosonic acid-depleted Escherichia coli

The Escherichia coli K-12 strain KPM22, defective in synthesis of 3-deoxy-d- manno -oct-2-ulosonic acid (Kdo), is viable with an outer membrane (OM) composed predominantly of lipid IV A , a precursor of lipopolysaccharide (LPS) biosynthesis that lacks any glycosylation. To sustain viability, the presence of a second-site suppressor was proposed for transport of lipid IV A from the inner membrane (IM), thus relieving toxic side-effects of lipid IV A accumulation and providing sufficient amounts of LPS precursors to support OM biogenesis. We now report the identification of an arginine to cysteine substitution at position 134 of the conserved IM protein YhjD in KPM22 that acts as a compensatory suppressor mutation of the lethal δKdo phenotype. Further, the yhjD400 suppressor allele renders the LPS transporter MsbA dispensable for lipid IV A transmembrane trafficking. The independent derivation of a series of non-conditional KPM22-like mutants from the Kdo-dependent parent strain TCM15 revealed a second class of suppressor mutations localized to MsbA. Proline to serine substitutions at either residue 18 or 50 of MsbA relieved the Kdo growth dependence observed in the isogenic wild-type strain. The possible impact of these suppressor mutations on structure and function are discussed by means of a computationally derived threading model of MsbA.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75126/1/MMI_6074_sm_Figure_S1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/75126/2/j.1365-2958.2007.06074.x.pd