A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order \Delta operator in antisymplectic geometry, which in general has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsionfree connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in a curved Riemannian space.Comment: 55 pages, LaTeX. v2: Subsection 3.10 expanded. v3: Reference added. v4: Published versio

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.Comment: 20 pages, 9 image

Cohomology of Filippov algebras and an analogue of Whitehead's lemma

We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whitehead's Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.Comment: plain latex, no figures, 29 page

Symplectic connections and Fedosov's quantization on supermanifolds

A (biased and incomplete) review of the status of the theory of symplectic connections on supermanifolds is presented. Also, some comments regarding Fedosov's technique of quantization are made.Comment: Submitted to J. of Phys. Conf. Se

Cosmological tachyon from cubic string field theory

The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the stability of the cosmological perturbations, and the relation between this tachyon and the Dirac-Born-Infeld one.Comment: 20 pages JHEP style, 1 figure; v4: misprints corrected, matches the published versio

Noncommutative Dipole Field Theories And Unitarity

We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.Comment: typos corrected, more details added in Sec 5, version to appear in JHE

On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes-Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra-Itzykson-Zuber integral.Comment: 20 pages, LaTeX. v2: minor corrections. v3: Added an Appendix about Harish-Chandra-Itzykson-Zuber integrals. v4: Added Reference

Investigation of a Light Gas Helicon Plasma Source for the VASIMR Space Propulsion System

An efficient plasma source producing a high-density (approx.10(exp 19/cu m) light gas (e.g. H, D, or He) flowing plasma with a high degree of ionization is a critical component of the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) concept. We are developing an antenna to apply ICRF power near the fundamental ion cyclotron resonance to further accelerate the plasma ions to velocities appropriate for space propulsion applications. The high degree of ionization and a low vacuum background pressure are important to eliminate the problem of radial losses due to charge exchange. We have performed parametric (e.g. gas flow, power (0.5 - 3 kW), magnetic field , frequency (25 and 50 MHz)) studies of a helicon operating with gas (H2 D2, He, N2 and Ar) injected at one end with a high magnetic mirror downstream of the antenna. We have explored operation with a cusp and a mirror field upstream. Plasma flows into a low background vacuum (<10(exp -4) torr) at velocities higher than the ion sound speed. High densities (approx. 10(exp 19/cu m) have been achieved at the location where ICRF will be applied, just downstream of the magnetic mirror

On God-Belief and Feeling Clean

Recent work has shown robust associations between morality and cleanliness. However, it is not known whether this association is equally consequential for everyone. I predicted that individuals high (vs. low) in God-belief would be more likely to draw upon feelings of cleanliness to represent their moral concerns. To test this hypothesis, I used a 2-week daily sampling protocol. In an initial session, I measured participants’ ( N = 135) level of God-belief. I then measured participants’ levels of daily cleanliness, neuroticism, impulsivity, and prosocial behaviors every evening. Daily feelings of cleanliness predicted lower levels of neuroticism but only for those high in God-belief. Daily impulsive behaviors predicted lower feelings of cleanliness, and daily prosocial behaviors predicted higher feelings of cleanliness. God-belief moderated these effects such that they were stronger for those higher, than lower, in God-belief. In closing, I discuss potential reasons for these moderation effects and other theoretical considerations. </jats:p