A gauge theory of quantum mechanics

An Abelian gerbe is constructed over classical phase space. The 2-cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincare-Cartan form. The U(1) gauge group on the gerbe has a natural interpretation as the invariance group of the Schroedinger equation on phase space.Comment:

The Cretaceous-Tertiary boundary marine extinction and global primary productivity collapse

The extinction of marine phyto-and zoo-plankton across the K-T boundary has been well documented. Such an event may have resulted in decreased photosynthetic fixation of carbon in surface waters and a collapse of the food chain in the marine biosphere. Because the vertical and horizontal distribution of the carbon isotopic composition of total dissolved carton (TDC) in the modern ocean is controlled by the transfer of organic carbon from the surface to deep reservoirs, it follows that a major disruption of the marine biosphere would have had a major effect on the distribution of carbon isotopes in the ocean. Negative carbon isotope excursions have been identified at many marine K-T boundary sequences worldwide and are interpreted as a signal of decreased oceanic primary productivity. However, the magnitude, duration and consequences of this productivity crisis have been poorly constrained. On the basis of planktonic and benthic calcareous microfossil carbon isotope and other geochemical data from DSDP Site 577 located on the Shatsky Rise in the north-central Pacific, as well as other sites, researchers have been able to provide a reasonable estimate of the duration and magnitude of this event

A Classical Bound on Quantum Entropy

A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, involving the variance $\sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio

Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations

The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as Feynman's approach. This allows us to go beyond the standard case and discover non-trivial results. In fact, while the first formulation gives rise to the static Maxwell equations, the second formulation is based on the following assumption $m[x_{j},\dot{x_{k}}]=i\hbar \delta_{jk}+im\theta_{jk}f.$ The results extracted from the second formulation are more significant since they are associated to a non trivial $\theta$-extension of the Bianchi-set of Maxwell equations. We find $div_{\theta}B=\eta_{\theta}$ and $\frac{\partial B_{s}}{\partial t}+\epsilon_{kjs}\frac{\partial E_{j}}{\partial x_{k}}=A_{1}\frac{d^{2}f}{dt^{2}}+A_{2}\frac{df}{dt}+A_{3},$ where $\eta_{\theta}$, $A_{1}$, $A_{2}$ and $A_{3}$ are local functions depending on the NC $\theta$-parameter. The novelty of this proof in the NC space is revealed notably at the level of the corrections brought to the previous Maxwell equations. These corrections correspond essentially to the possibility of existence of magnetic charges sources that we can associate to the magnetic monopole since $div_{\theta}B=\eta_{\theta}$ is not vanishing in general.Comment: LaTeX file, 16 page

Supporting reflection and creative thinking by carers of older people with dementia

This vision paper frames requirements engineering as a creative problem solving process. Its purpose is to enable requirements researchers and practitioners to recruit relevant theories, models, techniques and tools from creative problem solving to understand and support requirements processes more effectively. It uses 4 drivers to motivate the case for requirements engineering as a creative problem solving process. It then maps established requirements activities onto one of the longest-established creative problem solving processes, and uses these mappings to locate opportunities for the application of creative problem solving in requirements engineering. The second half of the paper describes selected creativity theories, techniques, software tools and training that can be adopted to improve requirements engineering research and practice. The focus is on support for problem and idea finding - two creative problem solving processes that our investigation revealed are poorly supported in requirements engineering. The paper ends with a research agenda to incorporate creative processes, techniques, training and tools in requirements projects

Introducing creativity techniques and software apps to the care of people with dementia

This poster reports research to introduce creative problem solving techniques and software to the care for people with dementia in residential homes

Evoking Emotion through Stories in Creative Dementia Care

This paper reports research to refine the design of a mobile creativity support app to improve person-centred care for older people with dementia. One barrier to previous app use during creative thinking appeared to be the negative activation emotions associated with problem avoidance and prevention exhibited by care staff when resolving challenging behaviours. Therefore we investigated the redesign of the app’s content so that care staff were more likely to positive activation associated with creative thinking through storytelling through a first formative evaluation

Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides--coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.Comment: LaTeX, 22 pages, 2 figure

Currents, Charges, and Canonical Structure of Pseudodual Chiral Models

We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of the pseudodual model, both local and nonlocal, as transmutations of the symmetries of the usual chiral model. We refine the conventional algorithm to more efficiently produce the nonlocal symmetries of the model, and we discuss the complete local current algebra for the pseudodual theory. We also exhibit the canonical transformation which connects the usual chiral model to its fully equivalent dual, further distinguishing the pseudodual theory.Comment: 15 pages, ANL-HEP-PR-93-85,Miami-TH-1-93,Revtex (references updated, format improved to Revtex

Dirac brackets from magnetic backgrounds

In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalised complex geometry, such magnetic terms in the symplectic form arise naturally by means of B-transformations. Here we prove that, regarding classical phase space as a generalised complex manifold, the transformation law for the symplectic form under the action of a weak magnetic field gives rise to Dirac's prescription for Poisson brackets in the presence of constraints.Comment: 9 page