On Finite 4D Quantum Field Theory in Non-Commutative Geometry

The truncated 4-dimensional sphere $S^4$ and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping the SO(5) symmetry and the finite number of degrees of freedom. The usual field theory UV-divergences are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove

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

The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4

We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and the divergent contributions corrected accordingly. As a result the model turns out to be asymptotically fre

The Fuzzy Ginsparg-Wilson Algebra: A Solution of the Fermion Doubling Problem

The Ginsparg-Wilson algebra is the algebra underlying the Ginsparg-Wilson solution of the fermion doubling problem in lattice gauge theory. The Dirac operator of the fuzzy sphere is not afflicted with this problem. Previously we have indicated that there is a Ginsparg-Wilson operator underlying it as well in the absence of gauge fields and instantons. Here we develop this observation systematically and establish a Dirac operator theory for the fuzzy sphere with or without gauge fields, and always with the Ginsparg-Wilson algebra. There is no fermion doubling in this theory. The association of the Ginsparg-Wilson algebra with the fuzzy sphere is surprising as the latter is not designed with this algebra in mind. The theory reproduces the integrated U(1)_A anomaly and index theory correctly.Comment: references added, typos corrected, section 4.2 simplified. Report.no: SU-4252-769, DFUP-02-1

A compact and robust diode laser system for atom interferometry on a sounding rocket

We present a diode laser system optimized for laser cooling and atom interferometry with ultra-cold rubidium atoms aboard sounding rockets as an important milestone towards space-borne quantum sensors. Design, assembly and qualification of the system, combing micro-integrated distributed feedback (DFB) diode laser modules and free space optical bench technology is presented in the context of the MAIUS (Matter-wave Interferometry in Microgravity) mission. This laser system, with a volume of 21 liters and total mass of 27 kg, passed all qualification tests for operation on sounding rockets and is currently used in the integrated MAIUS flight system producing Bose-Einstein condensates and performing atom interferometry based on Bragg diffraction. The MAIUS payload is being prepared for launch in fall 2016. We further report on a reference laser system, comprising a rubidium stabilized DFB laser, which was operated successfully on the TEXUS 51 mission in April 2015. The system demonstrated a high level of technological maturity by remaining frequency stabilized throughout the mission including the rocket's boost phase

System Tests of the ATLAS Pixel Detector

The innermost part of the ATLAS (A Toroidal LHC ApparatuS) experiment at the LHC (Large Hadron Collider) will be a pixel detector, which is presently under construction. Once installed into the experimental area, access will be extremely limited. To ensure that the integrated detector assembly operates as expected, a fraction of the detector which includes the power supplies and monitoring system, the optical readout, and the pixel modules themselves, has been assembled and operated in a laboratory setting for what we refer to as system tests. Results from these tests are presented.Comment: 5 Pages, 9 Figures, to appear in Proceedings of the Eleventh Workshop on Electronics for LHC and Future Experiment

BaFe_{1.8}Co_{0.2}As_2 thin film hybrid Josephson junctions

Josephson junctions with iron pnictides open the way for fundamental experiments on superconductivity in these materials and their application in superconducting devices. Here, we present hybrid Josephson junctions with a BaFe_{1.8}Co_{0.2}As_2 thin film electrode, an Au barrier and a PbIn counter electrode. The junctions show RSJ-like current-voltage characteristics up to the critical temperature of the counter electrode of about 7.2K. The temperature dependence of the critical current, IC, does not show an Ambegaokar-Baratoff behavior. Well-pronounced Shapiro steps are observed at microwave frequencies of 10-18GHz. Assuming an excess current, I_ex, of 200 {\mu}A at 4.2K we get an effective I_C R_N product of 6 {\mu}V.Comment: submitted to Appl. Phys. Let

Self similar Barkhausen noise in magnetic domain wall motion

A model for domain wall motion in ferromagnets is analyzed. Long-range magnetic dipolar interactions are shown to give rise to self-similar dynamics when the external magnetic field is increased adiabatically. The power spectrum of the resultant Barkhausen noise is of the form $1/\omega^\alpha$, where $\alpha\approx 1.5$ can be estimated from the critical exponents for interface depinning in random media.Comment: 7 pages, RevTex. To appear in Phys. Rev. Let

L-functions of Symmetric Products of the Kloosterman Sheaf over Z

The classical $n$-variable Kloosterman sums over the finite field ${\bf F}_p$ give rise to a lisse $\bar {\bf Q}_l$-sheaf ${\rm Kl}_{n+1}$ on ${\bf G}_{m, {\bf F}_p}={\bf P}^1_{{\bf F}_p}-\{0,\infty\}$, which we call the Kloosterman sheaf. Let $L_p({\bf G}_{m,{\bf F}_p}, {\rm Sym}^k{\rm Kl}_{n+1}, s)$ be the $L$-function of the $k$-fold symmetric product of ${\rm Kl}_{n+1}$. We construct an explicit virtual scheme $X$ of finite type over ${\rm Spec} {\bf Z}$ such that the $p$-Euler factor of the zeta function of $X$ coincides with $L_p({\bf G}_{m,{\bf F}_p}, {\rm Sym}^k{\rm Kl}_{n+1}, s)$. We also prove similar results for $\otimes^k {\rm Kl}_{n+1}$ and $\bigwedge^k {\rm Kl}_{n+1}$.Comment: 16 page