Apprenticeship for 'Liquid Life': Learning in Contingent Work Conditions for Contingent Employment

Taking the distinction between the Institution of Apprenticeship, that is, the social partnership arrangements which underpin its organisation, and Apprenticeship as a Social Model of Learning, in other words, he configuration of pedagogic and occupational etc. dimensions which constitute the model, as its starting point the paper: (i) argues the emergence of de-centred, distributed and discontinuous conditions associated with project-work present challenges for extant ideas about apprenticeship as a social model of learning; (ii) explores this claim in relation to Fuller and Unwin’s four inter-connected dimensions of apprenticeship as a social model of learning by considering a case study of apprenticeship designed to prepare apprentices to work in the above conditions; (iii) relates issues arising from the case study to research on project work from the fields of Organisational and Cultural Studies; and (iv) based on this evidence base introduces a typology of ‘Apprenticeship for Liquid Life’

Solving Potential Scattering Equations without Partial Wave Decomposition

Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a partial-wave expansion. We illustrate this procedure for the Bethe-Salpeter equation for pion-nucleon scattering and give explicit details for the one-nucleon-exchange term in the potential. Finally, we show how this method can be applied to pion photoproduction from the nucleon with $\pi N$ rescattering being treated so as to maintain unitarity to first order in the electromagnetic coupling. The procedure for removing the azimuthal angle dependence becomes increasingly complex as the spin of the particles involved increases.Comment: 15 pages, 4 figure

'It's not like a normal 9 to 5!': the learning journeys of media production apprentices in distributed working conditions

An apprenticeship in media production in England is at the centre of this case study exploration. The context is exemplified by the organisation of the process of production around project teams and the development of project-based working cultures. Given these developments, the working conditions and learning opportunities presented to apprentices can be characterised as de-centred and distributed. This contrasts with the characterisation of apprentices’ learning as novices who develop expertise in stable, well-bounded vocational communities. Through an analysis of young apprentices’ journeys, we argue that despite the challenges presented, the case study exemplifies the extent to which the apprenticeship is capable of innovation in project working as opposed to full employment conditions. Through its focus on media apprentices’ journeys, this paper makes visible the specific experience of learning in project working, distributed and de-centred working conditions. We conclude by referring to an ideal typical conception of the model of learning underpinning the apprenticeship which may be useful as an heuristic tool for others involved in designing and/or researching apprenticeships in project working conditions

Unitarity and the Bethe-Salpeter Equation

We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $\phi^2\sigma$ interaction Lagrangian and the $\pi N$ system with $s$-, $u$-, and $t$-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in Phys. Rev.

Restoration of rotational invariance of bound states on the light front

We study bound states in a model with scalar nucleons interacting via an exchanged scalar meson using the Hamiltonian formalism on the light front. In this approach manifest rotational invariance is broken when the Fock space is truncated. By considering an effective Hamiltonian that takes into account two meson exchanges, we find that this breaking of rotational invariance is decreased from that which occurs when only one meson exchange is included. The best improvement occurs when the states are weakly bound.Comment: 20 pages, 6 figures, uses feynMF; changed typos, clarified use of angular momentu

Solution of the Bethe-Salpeter equation for pion-nucleon scattering

A relativistic description of pion-nucleon scattering based on the four-dimensional Bethe-Salpeter equation is presented. The kernel of the equation consists of s- and u-channel nucleon and delta pole diagrams, as well as rho and sigma exchange in the t-channel. The Bethe-Salpeter equation is solved by means of a Wick rotation, and good fits are obtained to the s- and p-wave phase shifts up to 360 MeV pion laboratory energy. The coupling constants determined by the fits are consistent with the commonly accepted values in the literature.Comment: 34 pages, RevTeX; 7 figures. Several references added, a few typos corrected. Accepted for publication in Physical Review

Role of retardation in 3-D relativistic equations

Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been used within the framework of $\phi^2\sigma$ coupling to study the role of energy dependence and non-locality when the two-body potential is the sum of $\sigma$-exchange and crossed $\sigma$ exchange. The results show that non-locality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.Comment: 17 pages, RevTeX; 8 figures. Accepted for publication in Phys. Rev. C56 (Nov. 97