Quantum symmetries and the Weyl-Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase-space. Each such phase-space representation is a Weyl-Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by `factorising' the Weyl-Wigner product. However, not every real, unitary representation on phase-space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl-Wigner product and can be factorised. The conditions under which this is possible are examined. Examples are presented.Comment: Latex2e file, 37 page

Plasma accelerator Patent

Crossed-field plasma accelerator for laboratory simulation of atmospheric reentry condition

A dynamical symmetry breaking model in Weyl space

The dynamical process following the breaking of Weyl geometry to Riemannian geometry is considered by studying the motion of de Sitter bubbles in a Weyl vacuum. The bubbles are given in terms of an exact, spherically symmetric thin shell solution to the Einstein equations in a Weyl-Dirac theory with a time-dependent scalar field of the form beta = f(t)/r. The dynamical solutions obtained lead to a number of possible applications. An important feature of the thin shell model is the manner in which beta provides a connection between the interior and exterior geometries since information about the exterior geometry is contained in the boundary conditions for beta.Comment: 18 pages, RevTex, to be published in J. Math. Phy

Non-positivity of the Wigner function and bounds on associated integrals

The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval [0,1]. The problem of finding best-possible upper and lower bounds for a given region is the problem of finding the greatest and least eigenvalues of an associated Hermitian operator. Exactly solvable examples are described, and possible extensions are indicated.Comment: 5 pages, Latex2e fil

A Coronal Hole's Effects on CME Shock Morphology in the Inner Heliosphere

We use STEREO imagery to study the morphology of a shock driven by a fast coronal mass ejection (CME) launched from the Sun on 2011 March 7. The source region of the CME is located just to the east of a coronal hole. The CME ejecta is deflected away from the hole, in contrast with the shock, which readily expands into the fast outflow from the coronal hole. The result is a CME with ejecta not well centered within the shock surrounding it. The shock shape inferred from the imaging is compared with in situ data at 1 AU, where the shock is observed near Earth by the Wind spacecraft, and at STEREO-A. Shock normals computed from the in situ data are consistent with the shock morphology inferred from imaging.Comment: to appear in The Astrophysical Journa

A Blockchain-based Approach for Data Accountability and Provenance Tracking

The recent approval of the General Data Protection Regulation (GDPR) imposes new data protection requirements on data controllers and processors with respect to the processing of European Union (EU) residents' data. These requirements consist of a single set of rules that have binding legal status and should be enforced in all EU member states. In light of these requirements, we propose in this paper the use of a blockchain-based approach to support data accountability and provenance tracking. Our approach relies on the use of publicly auditable contracts deployed in a blockchain that increase the transparency with respect to the access and usage of data. We identify and discuss three different models for our approach with different granularity and scalability requirements where contracts can be used to encode data usage policies and provenance tracking information in a privacy-friendly way. From these three models we designed, implemented, and evaluated a model where contracts are deployed by data subjects for each data controller, and a model where subjects join contracts deployed by data controllers in case they accept the data handling conditions. Our implementations show in practice the feasibility and limitations of contracts for the purposes identified in this paper

The Development of a Direct Homologous Radioimmunoassay for Serum Cortisol

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