No abstract

The irreducible components of the curvature under the Lorentz group are of direct physical relevance in the four-dimensional Riemannian geometry of general relativity. The same is true for both curvature and torsion in the four-dimensional Riemann-Cartan geometry of the Poincare gauge theory of gravitation. In the latter theory a knowledge of these irreducible components is also extremely useful when setting up the Lagrangian and searching for exact solutions. The author deals with an n-dimensional metric-affine spacetime of arbitrary signature. In such a spacetime the connection is no longer metric so that there is an additional geometric object-the nonmetricity. The irreducible decompositions of nonmetricity, torsion and curvature under the pseudo-orthogonal group as well as those of the corresponding Bianchi identities are derived. Because of the increasing use made of it in the literature, the exterior form notation is used throughout.

Einstein's general relativity theory describes very well the gravitational phenomena in the macroscopic world. In the microscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for a renormalizable field theory. We argue that the local extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to a GL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status of independent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein "s GR surfaces as an effective "lowenergy" theory.

The detection and recording of vibration emission from human joints, a technique which we have termed "vibration arthrography", is a sensitive, non-invasive method for the objective study of the locomotor system. Using vibration sensors attached to bony prominences around the knee, we studied the joints of both normal and symptomatic subjects. Normal subjects produced three signal types-physiological patellofemoral crepitus, patellar clicks, and the lateral band signal. In symptomatic subjects we indentifled and categorised many signal types and related them to pathology. Lesions of the menisci produced distinctive signals, and it was possible not only to lateralise the tear, but in many cases to determine the type of meniscal injury present. Vibration arthrography promises to be a useful tool in the non-invasive diagnosis of knee disorders.