Non-commutative Complex Projective Spaces and the Standard Model

The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes' non-commutative geometry and making the complex spaces `fuzzy' a matrix approximation to the fuzzy space allows for three generations to emerge. The generations are associated with three copies of space-time. Higgs' fields and Yukawa couplings can be accommodated in the usual way.Comment: Contribution to conference in honour of A.P. Balachandran's 65th birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTe

Hardening electronic devices against very high total dose radiation environments

The possibilities and limitations of hardening silicon semiconductor devices to the high neutron and gamma radiation levels and greater than 10 to the eighth power rads required for the NERVA nuclear engine development are discussed. A comparison is made of the high dose neutron and gamma hardening potential of bipolar, metal insulator semiconductors and junction field effect transistors. Experimental data is presented on device degradation for the high neutron and gamma doses. Previous data and comparisons indicate that the JFET is much more immune to the combined neutron displacement and gamma ionizing effects than other transistor types. Experimental evidence is also presented which indicates that p channel MOS devices may be able to meet the requirements

The Distribution of Fox Squirrel (Sciurus niger) Leaf Nests within Forest Fragments in Central Indiana

We examined the abundance and placement of leaf nests by fox squirrels in six urban woodlots in central Indiana ranging in size from 1.06 to 8.28 ha. Four of the woodlots were disturbed, or subject to extensive human impact, whereas the remaining two were nature preserves. We counted all leaf nests present in each woodlot and recorded nest tree characteristics. We then conducted a quantitative vegetation analysis of trees present and estimated percentages of herbaceous and shrub cover along a minimum of two 100 m transects at each site. Fox squirrels showed a preference to build nests in certain species of trees. However, preference for nest tree species was not consistent across sites. Fox squirrels preferred to build nests in large trees with vines in the canopy at all sites. Characteristics of nests and nest trees did not differ among sites, but nest density was greater in the disturbed sites compared to the nature preserve sites. The nature preserve sites differed from the disturbed sites only with regard to the amount of shrub and herbaceous cover; shrub cover was greater and herbaceous cover was less at the disturbed sites. Results of this study suggest that fox squirrels are flexible with regard to nest tree species used and that the choice of a nest tree is dependent, in part, on tree size and the presence of vines. Further, a higher density of leaf nests in disturbed woodlots suggests that habitat disturbance and fragmentation due to urbanization may not have detrimental effects on the abundance and persistence of fox squirrels

A projective Dirac operator on CP^2 within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos correcte

The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit

It is well established that the response of a black hole to a generic perturbation is characterized by a spectrum of damped resonances, called quasinormal modes; and that, in the limit of large angular momentum ($l \gg 1$), the quasinormal mode frequency spectrum is related to the properties of unstable null orbits. In this paper we develop an expansion method to explore the link. We obtain new closed-form approximations for the lightly-damped part of the spectrum in the large-$l$ regime. We confirm that, at leading order in $l$, the resonance frequency is linked to the orbital frequency, and the resonance damping to the Lyapunov exponent, of the relevant null orbit. We go somewhat further than previous studies to establish (i) a spin-dependent correction to the frequency at order $1 / l$ for equatorial ($m = \pm l$) modes, and (ii) a new result for polar modes ($m = 0$). We validate the approach by testing the closed-form approximations against frequencies obtained numerically with Leaver's method.Comment: 18 pages, 3 tables, 3 figure

Instability of the massive Klein-Gordon field on the Kerr spacetime

We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M \mu \lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $\tau^{-1} \approx 1.5 \times 10^{-7} (GM/c^3)^{-1}$, at $M \mu \approx 0.42$. The physical implications are discussed.Comment: Added references. 27 pages, 7 figure

Simulation of a scalar field on a fuzzy sphere

The phi^4 real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a disordered phase, and a non-uniform ordered phase where the spatial SO(3) symmetry of the round sphere is spontaneously broken and which has no classical equivalent. The three coexistence lines between these phases, which meet at a triple point, are carefully located with particular attention paid to the one between the two ordered phases and the triple point itself. In the neighbourhood of the triple point all phase boundaries are well approximated by straight lines which, surprisingly, have the same scaling. We argue that unless an additional term is added to enhance the effect of the kinetic term the infinite matrix limit of this model will not correspond to a real scalar field on the commutative sphere or plane.Comment: 30 pages, 10 figures, accepted in International Journal of Modern Physics

Self-Dual Action for Fermionic Fields and Gravitation

This paper studies the self-dual Einstein-Dirac theory. A generalization is obtained of the Jacobson-Smolin proof of the equivalence between the self-dual and Palatini purely gravitational actions. Hence one proves equivalence of self-dual Einstein-Dirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac theory. The Bianchi symmetry of the curvature, core of the proof, now contains a non-vanishing torsion. Thus, in the self-dual framework, the extra terms entering the equations of motion with respect to the standard Einstein-Dirac field equations, are neatly associated with torsion.Comment: 13 pages, plain-tex, recently appearing in Nuovo Cimento B, volume 109, pages 973-982, September 199

Emotion-induced retrograde amnesia varies as a function of noradrenergic-glucocorticoid activity

RATIONALE: Privileged episodic encoding of an aversive event often comes at a cost of neutral events flanking the aversive event, resulting in decreased episodic memory for these neutral events. This peri-emotional amnesia is amygdala-dependent and varies as a function of norepinephrine activity. However, less is known about the amnesiogenic potential of cortisol. OBJECTIVE: We used a strategy of pharmacologically potentiating cortisol and norepinephrine activity to probe the putative neurochemical substrates of peri-emotional amnesia. MATERIALS AND METHODS: Fifty-four healthy individuals participated in a randomized double-blind placebo-controlled study. Within the experimental context of an established peri-emotional amnesia paradigm, we tested the amnesiogenic potential of hydrocortisone (30 mg p.o.) in the presence or absence of the norepinephrine-reuptake inhibitor reboxetine (4 mg p.o.). RESULTS: Under dual challenge conditions, we observed a linear dose-response relationship in the magnitude and duration of emotion-induced retrograde amnesia. CONCLUSIONS: Our results are consistent with a phenotypic expression of retrograde amnesia varying as a function of norepinephrine and cortisol coactivation during episodic encoding of aversive events. Our study demonstrates that the adverse cognitive and behavioral sequelae of aversive emotion can be experimentally modeled by a pharmacological manipulation of its putative neurochemical substrates

Resistivity peak values at transition between fractional quantum Hall states

Experimental data available in the literature for peak values of the diagonal resistivity in the transitions between fractional quantum Hall states are compared with the theoretical predictions. It is found that the majority of the peak values are close to the theoretical values for two-dimensional systems with moderate mobilities.Comment: 3 pages, 1 figur