Fermion Zero Modes in Odd Dimensions

We study the zero modes of the Abelian Dirac operator in any odd dimension. We use the stereographic projection between a $(2n-1)$ dimensional space and a $(2n-1)$ sphere embedded in a $2n$ dimensional space. It is shown that the Dirac operator with a gauge field of uniform field strengths in $S^{2n-1}$ has symmetries of SU($n$)$\times$U(1) which is a subgroup of SO($2n$). Using group representation theory, we obtain the number of fermion zero modes, as well as their explicit forms, in a simple way.Comment: 14 page

Mineralogy and Elemental Composition of Wind Drift Soil at Rocknest, Gale Crater

The Mars Science Laboratory rover Curiosity has been exploring Mars since August 5, 2012, conducting engineering and first-time activities with its mobility system, arm, sample acquisition and processing system (SA/SPaH-CHIMRA) and science instruments. Curiosity spent 54 sols at a location named "Rocknest," collecting and processing five scoops of loose, unconsolidated materials ("soil") acquired from an aeolian bedform (Fig. 1). The Chemistry and Mineralogy (CheMin) instrument analyzed portions of scoops 3, 4, and 5, to obtain the first quantitative mineralogical analysis of Mars soil, and to provide context for Sample Analysis at Mars (SAM) measurements of volatiles, isotopes and possible organic materials