Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz's wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p,Q)=(2,0) corresponds to a deformed Jacobi group and describes Lichnerowicz's original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p,Q)=(0,1) is simply the {\cal N}=1 superparticle whose supercharge amounts to the Dirac operator acting on spinors. The (2p,Q)=(0,2) model is the {\cal N}=2 supersymmetric quantum mechanics corresponding to differential forms. (This latter pair of models are supersymmetric on any Riemannian background.) When Q is odd, the models apply to spinor-tensors. The (2p,Q)=(2,1) model is distinguished by admitting a central Lichnerowicz-Dirac operator when the background is constant curvature. The new supersymmetric models are novel in that the Hamiltonian is not just a square of super charges, but rather a sum of commutators of supercharges and commutators of bosonic charges. These models and superalgebras are a very useful tool for any study involving high rank tensors and spinors on manifolds.Comment: 39 pages, LaTeX, fixed typos, added refs, final version to appear in CM

The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra

Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric tensor bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R). These results have already been generalized by the authors to arbitrary tensor and spinor bundles using supersymmetric quantum mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric tensor setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering

Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. We present a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang--Mills detour complex, which recently has been applied in the mathematical setting of conformal geometry. An analysis of asymptotic scattering states about the trivial field theory vacuum in the simplest version of the theory yields a rich spectrum marred by negative norm excitations. The result is a theory of a physical massless graviton, scalar field, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector of the model do have positive norms, but their evolution is no longer unitary and their amplitudes grow with time. The model is of considerable interest for braneworld scenarios and ghost condensation models, and invariant theory.Comment: 19 pages LaTe

Written versus verbal consent: a qualitative study of stakeholder views of consent procedures used at the time of recruitment into a peripartum trial conducted in an emergency setting.

BACKGROUND: Obtaining prospective written consent from women to participate in trials when they are experiencing an obstetric emergency is challenging. Alternative consent pathways, such as gaining verbal consent at enrolment followed, later, by obtaining written consent, have been advocated by some clinicians and bioethicists but have received little empirical attention. We explored women's and staff views about the consent procedures used during the internal pilot of a trial (GOT-IT), where the protocol permitted staff to gain verbal consent at recruitment. METHODS: Interviews with staff (n = 27) and participating women (n = 22). Data were analysed thematically and interviews were cross-compared to identify differences and similarities in participants' views about the consent procedures used. RESULTS: Women and some staff highlighted benefits to obtaining verbal consent at trial enrolment, including expediting recruitment and reducing the burden on those left exhausted by their births. However, most staff with direct responsibility for taking consent expressed extreme reluctance to proceed with enrolment until they had obtained written consent, despite being comfortable using verbal procedures in their clinical practice. To account for this resistance, staff drew a strong distinction between research and clinical care and suggested that a higher level of consent was needed when recruiting into trials. In doing so, staff emphasised the need to engage women in reflexive decision-making and highlighted the role that completing the consent form could play in enabling and evidencing this process. While most staff cited their ethical responsibilities to women, they also voiced concerns that the absence of a signed consent form at recruitment could expose them to greater risk of litigation were an individual to experience a complication during the trial. Inexperience of recruiting into peripartum trials and limited availability of staff trained to take consent also reinforced preferences for obtaining written consent at recruitment. CONCLUSIONS: While alternative consent pathways have an important role to play in advancing emergency medicine research, and may be appreciated by potential recruits, they may give rise to unintended ethical and logistical challenges for staff. Staff would benefit from training and support to increase their confidence and willingness to recruit into trials using alternative consent pathways. TRIAL REGISTRATION: This qualitative research was undertaken as part of the GOT-IT Trial (trial registration number: ISCRTN 88609453 ). Date of registration 26/03/2014

Constant Curvature Algebras and Higher Spin Action Generating Functions

The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R) [semidirect product] R^2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for the actions and gauge invariances of massive, partially massless and massless (for both bose and fermi statistics) higher spins on constant curvature backgrounds. These are formulated in terms of a minimal set of covariant, unconstrained, fields rather than towers of auxiliary fields. Partially massless gauge transformations are shown to arise as degeneracies of the flat, massless gauge transformation in one dimension higher. Moreover, our results and calculus offer a considerable simplification over existing techniques for handling higher spins. In particular, we show how theories of arbitrary spin in dimension d can be rewritten in terms of a single scalar field in dimension 2d where the d additional dimensions correspond to coordinate differentials. We also develop an analogous framework for spinor-tensor fields in terms of the corresponding superalgebra.Comment: 44 pages, LaTeX, 2 .eps figure

Prevention is better than cure, but...: Preventive medication as a risk to ordinariness?

Preventive health remains at the forefront of public health concerns; recent initiatives, such as the NHS health check, may lead to recommendations for medication in response to the identification of 'at risk' individuals. Little is known about lay views of preventive medication. This paper uses the case of aspirin as a prophylactic against heart disease to explore views among people invited to screening for a trial investigating the efficacy of such an approach. Qualitative interviews (N=46) and focus groups (N=5, participants 31) revealed dilemmas about preventive medication in the form of clashes between norms: first, in general terms, assumptions about the benefit of prevention were complicated by dislike of medication; second, the individual duty to engage in prevention was complicated by the need not to be over involved with one's own health; third, the potential appeal of this alternative approach to health promotion was complicated by unease about the implications of encouraging irresponsible behaviour among others. Though respondents made different decisions about using the drug, they reported very similar ways of trying to resolve these conflicts, drawing upon concepts of necessity and legitimisation and the special ordinariness of the particular dru

Cancer worry among Norwegian male BRCA1/2 mutation carriers

This qualitative study explored the experiences of Norwegian men after being identified as BRCA 1/2 mutation-positive. Only limited knowledge is available on this topic; therefore, the aim of this study was to gain a deeper insight from the men’s own perspectives. Data were collected from in-depth interviews with 15 men and seven of their partners. The participants described fear of cancer development, and two main narrative patterns were identified: fear for their own health, including fear of developing cancer, and negative feelings about responsibility for others’ health. The men expressed fear of developing cancer themselves and described a need for genetic risk information. They were also deeply concerned about how the mutation might affect their children and other relatives. There is a need for guidelines concerning genetic risk information and follow-up programs for male BRCA 1/2 mutation carriers. This study adds valuable contextual insights into their experiences of living with fear of cancer

Detours and Paths: BRST Complexes and Worldline Formalism

We construct detour complexes from the BRST quantization of worldline diffeomorphism invariant systems. This yields a method to efficiently extract physical quantum field theories from particle models with first class constraint algebras. As an example, we show how to obtain the Maxwell detour complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then we concentrate on first class algebras belonging to a class of recently introduced orthosymplectic quantum mechanical models and give generating functions for detour complexes describing higher spins of arbitrary symmetry types. The first quantized approach facilitates quantum calculations and we employ it to compute the number of physical degrees of freedom associated to the second quantized, field theoretical actions.Comment: 1+35 pages, 1 figure; typos corrected and references added, published versio