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

Virtual Braids

In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to all the categories in which braiding can be accomplished. We give a unifying topological interpretation of virtuals and flats (virtual strings) and their isotopies via ribbon surfaces and abstract link diagrams. We also give reduced presentations for the virtual braid group, the flat virtual braid group, the welded braid group and several other categories of braids. The paper includes a discussion of the topological intepretation of the welded braid group in terms of tubes embedded in four-space. A sequel to this paper will give a new proof of a Markov Theorem for virtual braids (and related categories) via the L-move (a technique pioneered for classical braids and braids in three-manifolds by the second author).Comment: 31 pages, 22 figures, LaTeX documen

BRST Detour Quantization

We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric and K\"ahler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form K\"ahler electromagnetism. We also discuss how our results generalize to other special geometries.Comment: 43 pages, LaTeX, added reference

Free singularity path planning of hybrid parallel robot

This paper presents a singularity-free path planning approach for a hybrid parallel robot. The hybrid robot is composed of two well-known parallel robots, a hexapod and a tripod, that are serially connected. In this paper a methodology is developed to avoid singularity configurations of the hybrid parallel robot. Nominal polynomial paths are used for motion of end effector, and the strokes of each actuator is calculated by using the developed inverse kinematic. A MATLAB program has been developed to generate the designed paths, and several poses have been tested in a CAD model of the hybrid parallel robot to validate the feasibility of the path planning approach

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

Virtual Knot Cobordism

This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots are given. Determinations of the four-ball genus of positive virtual knots are given using the results of a companion paper by the author and Heather Dye and Aaron Kaestner. Problems related to band-passing are explained, and a theory of isotopy of virtual surfaces is formulated in terms of a generalization of the Yoshikawa moves.Comment: 32 pages, 43 figures, LaTeX documen

Reconsidering feminisms and the work of Norbert Elias for understanding gender, sport and sport-related activities

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2008 North West Counties Physical Education Association and SAGE Publications.This paper reconsiders the relationships between feminist perspectives and the figurational/process-sociological perspective of Norbert Elias for understanding gender, sport and sport-related activities. The main aim of the article is to respond to Colwell's claim that there are differences between feminist and figurational approaches to understanding and explaining gender that potentially negate the possibility of being a feminist and figurational sociologist at the same time. The paper makes a contribution to the wider discussions about the adequacy of Elias's work in understanding gender and sport, and the potential of blending feminist and figurational perspectives on sport and gender. It introduces the principles underlying feminist and figurational approaches to sociology. The key features of the ongoing debate about the differences between feminist and figurational approaches are briefly outlined. I reply to Colwell's criticisms of my work and revisit issues surrounding the role of values and evaluation in sociology. Involved-detachment is introduced as a feminist interpretation of Elias's theory of ever changing balances of involvement-detachment. The final part of the paper presents some reflections about working with involved-detachment in specific research on women's involvement in sport-related fitness activities