Determination and Reduction of Large Diffeomorphisms

Within the Hamiltonian formulation of diffeomorphism invariant theories we address the problem of how to determine and how to reduce diffeomorphisms outside the identity component.Comment: 4 pages, Latex, macro espcrc2.sty. Contribution to the proceedings of the second conference on Constrained Dynamics and Quantum Gravity, Santa Margherita, Italy, 17-21 September 1996. To appear in Nucl. Phys. B Supp

The Spin-Statistics Connection in Quantum Gravity

It is well-known that is spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of "observables" is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian "charge" and "magnetic flux". We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also show how our approach fits into conventional formulations of quantum gravity.Comment: LaTeX file, 31 pages, 5 figure

Spinning Particles, Braid Groups and Solitons

We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of $M$ which is the relevant object for structureless particles. In particular, we compute these generalized braid groups for particles with an internal spin degree of freedom on an arbitrary $M$. A study of their unitary representations allows us to determine the available spectrum of spin and statistics on $M$ in a certain class of quantum theories. One interesting result is that half-integral spin quantizations are obtained on certain manifolds having an obstruction to an ordinary spin structure. We also compare our results to corresponding ones for topological solitons in $O(d+1)$-invariant nonlinear sigma models in $(d+1)$-dimensions, generalizing recent studies in two spatial dimensions. Finally, we prove that there exists a general scalar quantum theory yielding half-integral spin for particles (or $O(d+1)$ solitons) on a closed, orientable manifold $M$ if and only if $M$ possesses a ${\rm spin}_c$ structure.Comment: harvmac, 34 pages, HUTP-93/A037; UICHEP-TH/93-18; BUHEP-93-2

Mechanical properties of three-dimensional interconnected alumina/steel metal matrix composites

Three-dimensional interconnected alumina/steel metal matrix composites (MMCs) were produced by pressureless Ti-activated melt infiltration method using three types of Al2O3 powder with different sizes and shapes. By partial sintering during infiltration an interpenetrating ceramic network was realised. The effect of the ceramic particle size and shape on the resulting ceramic network, volume % fraction and the MMC properties is presented. The MMCs were characterised for mechanical properties at room temperature and elevated temperature. An increase in flexural strength and Young's modulus with decreasing particle size has been observed. In addition, the effect of the volume of ceramic content and the surface finish of the MMCs on the wear behaviour is show

Finite Approximations to Quantum Physics: Quantum Points and their Bundles

There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively reproduce important topological features of continuum physics like winding numbers and fractional statistics, and that too often with just a few points. In this work, we develop the essential tools for doing quantum physics on posets. The poset approach to covering space quantization, soliton physics, gauge theories and the Dirac equation are discussed with emphasis on physically important topological aspects. These ideas are illustrated by simple examples like the covering space quantization of a particle on a circle, and the sine-Gordon solitons.Comment: 24 pages, 8 figures on a uuencoded postscript file, DSF-T-29/93, INFN-NA-IV-29/93 and SU-4240-55