A geometric basis for the standard-model gauge group

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided ("exterior") and right-sided ("interior") types. By definition, Poincare transformations are exterior ones. We consider all rotations in the seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincare group and form the group SU(2)_L, interior ones that constitute SU(3)_C, and a unique group of coupled double-sided rotations with U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and isotopic symmetries within the restrictions of the Coleman--Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU(2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.Comment: 17 pages, LaTeX requires iopart. Accepted for publication in J. Phys. A: Math. Gen. 9 Mar 2001. Typos correcte

The Poincare mass operator in terms of a hyperbolic algebra

The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure.Comment: 5 pages Latex2

Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock Hypothesis and using these solutions, we are able to describe the space-time transformations between two uniformly accelerated and rotating systems.Comment: 15 pages 1 figur

Effect of temperature and relative humidity on the development times and survival of Synopsyllus fonquerniei and Xenopsylla cheopis, the flea vectors of plague in Madagascar

Acknowledgements We would like to thank Dr Lila Rahalison and Jocelyn Ratovonjato for their advice and help during the experiment. We are grateful to the staff of the Plague Unit and the Medical Entomology Unit at the Institut Pasteur de Madagascar, particularly Dr Nohal Elissa. Without their expertise this study would not have been possible. Sincere thanks to Mr Tojo Ramihangihajason for his technical assistance. We are indebted to the Institut Pasteur de Madagascar for an internal grant which facilitated additional laboratory research. Two Wellcome Trust fellowships supported ST during this work (081705 and 095171).Peer reviewedPublisher PD

A new view on relativity: Part 2. Relativistic dynamics

The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by introducing a new principle which is analogous to the Einstein's Equivalence Principle, but can be applied for any force. By this principle, the relativistic dynamic equation is defined by an element of the Lie algebra of the above representation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By the above principle, we show that the relativistic dynamic equation for the four-velocity leads to an analog of the electromagnetic tensor. This indicates that force in special relativity is described by a differential two-form

Spinors in the hyperbolic algebra

The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.Comment: 9 pages Latex2

A human approach to restructuring the education system: why schools in England need social pedagogy

In this article, we contend that the current schools’ system in England needs to be carefully reconsidered if we are to offer opportunities for success (in its broadest sense) to those whom our current, technocratic education system excludes. With a focus on social pedagogy and human-centred learning systems, we argue that continued modifications to the existing education system are no longer sufficient and that an ideology overhaul is needed before any significant positive progress can be made. To this end, we suggest various ways that schools might work towards developing healthier and more inclusive communities, built on the key social pedagogical foundations of positive relationships, democracy, inclusion, creativity and pedagogical love. We also make recommendations for an education system in which the teacher, as a highly trained professional, can enjoy a professional autonomy commensurate with their level of qualification. Finally, we dispel some of the myths that have prevented radical, community-focused change to date

Flock-level risk factors for scrapie in Great Britain: analysis of a 2002 anonymous postal survey

BACKGROUND: In November 2002, an anonymous postal survey of sheep farmers in Great Britain (GB) was conducted to identify factors associated with the flock-level occurrence of scrapie. This survey was undertaken to update an earlier postal survey in 1998, and was the first occasion in which a large-scale postal survey had been repeated. RESULTS: The results of the 2002 survey indicated that scrapie was more likely to occur in certain geographic regions; in purebred compared to commercial flocks; in larger flocks; in flocks which lambed in group pens compared to those which lambed in individual pens; in flocks which always lambed in the same location compared to those which did not; and in farms which kept certain breeds of sheep. In addition to these factors, the likelihood of the disease occurring in homebred animals was higher in flocks which bred a greater proportion of replacement animals or which bought-in lambs. Finally, within-flock transmission following exposure was more likely to occur in hill flocks compared to other farm types; in flocks which bred a greater proportion of replacement animals; and in farms which kept a certain crossbreed of ewe. CONCLUSION: The risk factors identified from the 1998 and 2002 anonymous postal surveys in Great Britain were similar. However, differences between the surveys were identified in the influence of region and of purchasing behaviour on the risk of scrapie. These differences are most likely a consequence of changes in farmer awareness and the impact of the 2001 foot-and-mouth disease epidemic, respectively

A second order differential equation for the relativistic description of electrons and photons

A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with a space-time algebra made up of Pauli matrices and hyperbolic numbers. The algebra is used to construct the differential operator of the electron as well as the photon wave equation. The properties of free electron and photon states related to this wave equation are investigated. Interactions are introduced as usual with the minimal substitution of the momentum operators. It can be shown that the new wave equation is equivalent to the quadratic form of the Dirac equation. Furthermore, the Maxwell equations can be derived from the corresponding wave equation for photons.Comment: Reverted preprint to initial version of 1999. Most of the content has been published under the new title "Relativistic quantum physics with hyperbolic numbers". However, interesting parts like the second quantization of fermion fields within a Klein-Gordon theory, which is only possible with the help of hyperbolic or bicomplex numbers, dropped out of the revised versio

Lightlike infinity in GCA models of Spacetime

This paper discusses a 7 dimensional conformal geometric algebra model for spacetime based on the notion that spacelike and timelike infinities are distinct. I show how naturally of the dimensions represents the lightlike infinity and appears redundant in computations, yet usefull in interpretationComment: 12 page