Gauging internal fermionic symmetries and spin 3/2 fields

Field theoretic models possessing a global internal fermionic shift symmetry are considered. When such a symmetry is realized locally, spin 3/2 fields appear naturally as gauge fields. Implementation of the gauging procedure requires not only the usual replacement of ordinary derivatives by covariant derivatives containing the spin 3/2 fields, but also the inclusion of additional monomials. The Higgs mechanism and the high energy Nambu-Goldstone fermion equivalence theorem are explicitly demonstrated.Comment: 9 page

Effective Constraints for Relativistic Quantum Systems

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which are extended here to relativistic systems as they arise for instance in quantum cosmology. By side-stepping explicit constructions of states, such tools allow one to arrive much more feasibly at results for physical observables at least in semiclassical regimes. Several questions discussed recently regarding effective equations and state properties in quantum cosmology, including the spreading of states and quantum back-reaction, are addressed by the examples studied here.Comment: 27 pages, 2 figures; v2: new appendix comparing effective constraints and physical coherent states by an exampl

Mindfulness: Mediating the Relationship between Attachment Security and Parenting Style

The current project examines the relationships between attachment security, parenting style, and mindfulness. The level of mindfulness an individual demonstrates is argued to mediate the relationship between an individual’s attachment security and her respective parenting style. The population is composed of 35 mothers who were drawn from a university clinic setting. Measures utilized included: the Relationship Questionnaire (RQ), which measures adult attachment security, the Mindful Attention Awareness Scale (MAAS), which measures the level of mindfulness an individual demonstrates, and the Parental Authority Questionnaire – Revised (PAQ-R), which measures parenting style attitudes. Results demonstrated no significant relationships between attachment security and parenting style. In examining the relationship between attachment security and mindfulness, individuals designated securely attached demonstrated higher levels of mindfulness than their insecure counterparts. With respect to mindfulness and its relationship with parenting style, mindfulness was positively correlated with an authoritative parenting style but did not demonstrate a significant relationship with either an authoritarian or a permissive parenting style. A test of mediation was conducted to examine the relationship between attachment security and parenting style, with mindfulness as the mediator. The model evidenced a significant reduction in the relationship between attachment security and an authoritative parenting style, suggesting that mindfulness successfully mediated this relationship. Mediation was not found in the case of the permissive and authoritarian styles. Discussions of the methodological approach, the implications of these findings, and future directions for research are presented

The 5-kW arcjet power electronics

The initial design and evaluation of a 5 kW arcjet power electronics breadboard which as been integrated with a modified 1 kW design laboratory arcjet is presented. A single stage, 5 kW full bridge, pulse width modulated (PWM), power converter was developed which was phase shift regulated. The converter used metal oxide semiconductor field effect transistor (MOSFET) power switches and incorporated current mode control and an integral arcjet pulse ignition circuit. The unoptimized power efficiency was 93.5 and 93.9 percent at 5 kW and 50A output at input voltages of 130 and 150V, respectively. Line and load current regulation at 50A output was within one percent. The converter provided up to 6.6 kW to the arcjet with simulated ammonia used as a propellant

Interactive Chemical Reactivity Exploration

Elucidating chemical reactivity in complex molecular assemblies of a few hundred atoms is, despite the remarkable progress in quantum chemistry, still a major challenge. Black-box search methods to find intermediates and transition-state structures might fail in such situations because of the high-dimensionality of the potential energy surface. Here, we propose the concept of interactive chemical reactivity exploration to effectively introduce the chemist's intuition into the search process. We employ a haptic pointer device with force-feedback to allow the operator the direct manipulation of structures in three dimensions along with simultaneous perception of the quantum mechanical response upon structure modification as forces. We elaborate on the details of how such an interactive exploration should proceed and which technical difficulties need to be overcome. All reactivity-exploration concepts developed for this purpose have been implemented in the Samson programming environment.Comment: 36 pages, 14 figure

Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements

We study the stability of quantum states of macroscopic systems of finite volume V, against weak classical noises (WCNs), weak perturbations from environments (WPEs), and local measurements (LMs). We say that a pure state is `fragile' if its decoherence rate is anomalously great, and `stable against LMs' if the result of a LM is not affected by another LM at a distant point. By making full use of the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile in any WCNs or WPEs. (ii) If square fluctuations of some additive operators are O(V^2) for a pure state, then it is fragile in some WCNs or WPEs. (iii) If a state (pure or mixed) has the `cluster property,' then it is stable against LMs, and vice versa. These results have many applications, among which we discuss the mechanism of symmetry breaking in finite systems.Comment: 6 pages, no figure.Proof of the theorem is described in the revised manuscrip

Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential

A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. To acomplish this, a similar path to the one used in the angular momentum case is employed; hence, the radial eigenfuntions calculated comprise non unitary representations of the algebra. One of the interesting properties of such non unitary representations is that they are not labeled by integer nor by half-integer numbers as happens in the usual angular momentum representation.Comment: 20 pages 1 eps figure in a single zipped file, submitted to J. Math. Phy

Canonical Quantization Inside the Schwarzschild Black Hole

We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to the need for CPT invariance to construct an explicitly positive definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum.Comment: 8 pages, LaTex. Title altered. One reference added. A few typos esp. eq.(7),(38) corrected. To appear in Class.Q.Gra

Symplectic map description of Halley's comet dynamics

The main features of 1P/Halley chaotic dynamics can be described by a two dimensional symplectic map. Using Mel'nikov integral we semi-analytically determine such a map for 1P/Halley taking into account gravitational interactions from the Sun and the eight planets. We determine the Solar system kick function ie the energy transfer to 1P/Halley along one passage through the Solar system. Our procedure allows to compute for each planet its contribution to the Solar system kick function which appears to be the sum of the Keplerian potential of the planet and of a rotating circular gravitational dipole potential due to the Sun movement around Solar system barycenter. We test the robustness of the symplectic Halley map by directly integrating Newton's equations over $\sim 2.4\cdot 10^4$ yr around Y2K and by reconstructing the Solar system kick function. Our results show that the Halley map with fixed parameters gives a reliable description of comet dynamics on time scales of $10^4$ yr while on a larger scales the parameters of the map are slowly changing due to slow oscillations of orbital momentum.Comment: To be published in Physics Letter A, 8 pages, 5 figures, supplementary material at http://perso.utinam.cnrs.fr/~lages/publications/sm/sm21.htm