Complex structures and the Elie Cartan approach to the theory of spinors

Each isometric complex structure on a 2$\ell$-dimensional euclidean space $E$ corresponds to an identification of the Clifford algebra of $E$ with the canonical anticommutation relation algebra for $\ell$ ( fermionic) degrees of freedom. The simple spinors in the terminology of E.~Cartan or the pure spinors in the one of C. Chevalley are the associated vacua. The corresponding states are the Fock states (i.e. pure free states), therefore, none of the above terminologies is very good.Comment: 10

Prototype ultrasonic instrument for quantitative testing

Ultrasonic instrument has been developed for use in quantitative nondestructive evaluation of material defects such as cracks, voids, inclusions, and unbonds. Instrument is provided with standard pulse source and transducer for each frequency range selected and includes integral aids that allow calibration to prescribed standards

Estimating moose population parameters from aerial surveys

Successful moose management depends on knowledge of population dynamics. The principal parameters required are size, rate of change, recruitment, sex composition, and mortality. Moose management in Alaska has been severely hampered by the lack of good estimates of these parameters, and unfortunately, this lack contributed to the decline of many Alaskan moose populations during the 1970s (e.g., Gasaway et al. 1983). The problems were: (1) population size not adequately estimated, (2) rapid rates of decline not acknowledged until populations were low, (3) meaningful recruitment rates were not available in the absence of good population estimates, and (4) calf and adult mortality rates were grossly underestimated. Frustration of moose managers working with inadequate data led to development of aerial survey procedures that yield minimally biased, sufficiently precise estimates of population parameters for most Alaskan moose management and research. This manual describes these procedures. Development of these procedures would have been impossible without the inspiration, support, advice, and criticism of many colleagues. We thank these colleagues for their contributions. Dale Haggstrom and Dave Kelleyhouse helped develop flight patterns, tested and improved early sampling designs, and as moose managers, put these procedures into routine use. Pilots Bill Lentsch and Pete Haggland were instrumental in developing and testing aerial surveying techniques. Their interest and dedication to improving moose management made them valuable allies. Statisticians Dana Thomas of the University of Alaska and W. Scott Overton of Oregon State University provided advice on variance approximations for the population estimator. Warren Ballard, Sterling Miller, SuzAnne Miller, Doug Larsen, and Wayne Kale tested procedures and provided valuable criticisms and suggestions. Jim Raymond initially programmed a portable calculator to make lengthy calculation simple, fast, and error-free. Angie Babcock, Lisa Ingalls, Vicky Leffingwell, and Laura McManus patiently typed several versions of this manual. John Coady and Oliver Burris provided continuous moral and financial support for a 3-year project that lasted 6 years. Joan Barnett, Rodney Boetje, Steven Peterson, and Wayne Regelin of the Alaska Department of Fish and Game provided helpful editorial suggestions in previous drafts. Finally, we thank referees David Anderson of the Utah Cooperative Wildlife Research Unit, Vincent Schultz of Washington State University, and James Peek, E. "Oz" Garton, and Mike Samuel of the University of Idaho whose comments and suggestions improved this manual. This project was funded by the Alaska Department of Fish and Game through Federal Aid in Wildlife Restoration Projects W-17-9 through W-22-1

N-complexes as functors, amplitude cohomology and fusion rules

We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.Comment: Final versio

Fractionalization of minimal excitations in integer quantum Hall edge channels

A theoretical study of the single electron coherence properties of Lorentzian and rectangular pulses is presented. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose charge and shape reflects the properties of interactions. We show that the dependence of fractionalization induced electron/hole pair production in the pulses amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses and an Hanbury Brown and Twiss interferometer to measure interaction induced electron/hole pair production and more generally to reconstruct single electron coherence of these excitations before and after their fractionalization.Comment: 18 pages, 10 figures, 1 tabl

Examples of derivation-based differential calculi related to noncommutative gauge theories

Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions". To appear in a special issue of International Journal of Geometric Methods in Modern Physic

The Origin of Chiral Anomaly and the Noncommutative Geometry

We describe the scalar and spinor fields on noncommutative sphere starting from canonical realizations of the enveloping algebra ${\cal A}={\cal U}{u(2))}$. The gauge extension of a free spinor model, the Schwinger model on a noncommutative sphere, is defined and the model is quantized. The noncommutative version of the model contains only a finite number of dynamical modes and is non-perturbatively UV-regular. An exact expresion for the chiral anomaly is found. In the commutative limit the standard formula is recovered.Comment: 30 page

BRS Cohomology of the Supertranslations in D=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $\delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot \beta} (\epsilon^{\mu})^{\dag}$. We find that the cohomology of this operator depends on a spin-orbit coupling in an SU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9

Massive spheroids can form in single minor mergers

Accepted for publication in MNRAS, 12 pages, 6 figuresUnderstanding how rotationally supported discs transform into dispersion-dominated spheroids is central to our comprehension of galaxy evolution. Morphological transformation is largely merger-driven. While major mergers can efficiently create spheroids, recent work has highlighted the significant role of other processes, like minor mergers, in driving morphological change. Given their rich merger histories, spheroids typically exhibit large fractions of ‘ex situ’ stellar mass, i.e. mass that is accreted, via mergers, from external objects. This is particularly true for the most massive galaxies, whose stellar masses typically cannot be attained without a large number of mergers. Here, we explore an unusual population of extremely massive (M ∗ > 10 11M) spheroids, in the Horizon-AGN simulation, which exhibit anomalously low ex situ mass fractions, indicating that they form without recourse to significant merging. These systems form in a single minor-merger event (with typical merger mass ratios of 0.11–0.33), with a specific orbital configuration, where the satellite orbit is virtually co-planar with the disc of the massive galaxy. The merger triggers a catastrophic change in morphology, over only a few hundred Myr, coupled with strong in situ star formation. While this channel produces a minority (∼5 per cent) of such galaxies, our study demonstrates that the formation of at least some of the most massive spheroids need not involve major mergers – or any significant merging at all – contrary to what is classically believed.Peer reviewedFinal Accepted Versio