Invariants of 2+1 gravity

In [1, 2] we established and dicussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genusg with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to 6g-6(g>1) is treated in detail with a precise classification forg=1 andg=2.     

Preparation and characterization of a set of IAEA reference air filters for quality control in air-pollution studies

Several sets of reference air filters were prepared as part of an IAEA evaluation of the performance of laboratories involved in air-pollution studies. Each set comprised three polycarbonate membrane filters, two of which were loaded with urban air particulate matter (APM) obtained in Vienna or Prague, and one unloaded filter. The filters were loaded by filtration of a suspension of the APM materials in water. The homogeneity both of bulk APM materials and of the loaded filters was evaluated and found suitable by determining several elements by instrumental neutron-activation analysis (INAA), proton-induced X-ray emission (PIXE), and micro-X-ray energy-dispersive fluorescence analysis (micro-EDXRF). After evaluation of the homogeneity, INAA, PIXE, EDXRF, atomic absorption spectrometry (AAS), inductively coupled plasma optical emission spectrometry (ICP-OES), and ICP mass spectrometry (ICP-MS) were used to characterize the filter materials and establish "target values" and their associated standard deviations for 15 elements. Problems encountered during the preparation of these unique, simulated air filters and the criteria for setting both the target values and standard deviations are presented.     

A new group theoretical technique for the analysis of Bianchi identities and its application to the auxiliary field problem of D = 5 supergravity

For any (super)group and hence for any geometrical (super)theory Bianchi identities imply that certain 3-forms vanish. In order to perform a systematic analysis of their implications in the presence of constraints one needs a complete basis of independent 3-forms spanning the 3-form linear space. In this paper we discuss a general procedure for the derivation of such a basis in the case of supersymmetric theories involving commuting spinor 1-forms. Our technique is based on the decomposition of the product of group representations into irreducible components and replaces all Fierz rearrangements. We give as examples the cases of N = 1, d = 4, N = 2, d = 4 and N = 2, d = 5 supergravity. Then applying our algebraic techniques to the last of these three models, the only other known example, besides N = 1, d = 4 supergravity, of a pure geometrical theory, we derive its off-shell structure containing 48 bosons and 48 fermions. The torsion-like constraints which we implement in the Bianchis in order to obtain our set of auxiliary fields are a subset of the complete set of variational equations of the theory so that we derive our off-shell multiplet without any reference to an embedding conformal symmetry. The point with which we still need to use ingenuity is the selection of those equations which are to be kept and those which are to be thrown out.     

The relativistic spherical top

The classical theory of the free relativistic spherical top is first developed from a Lagrangian viewpoint. Our method allows the invariant mass to be an arbitrary function of the intrinsic spin. A canonical formalism is established following the approach suggested by Dirac for constrained Hamiltonian systems. There is a second arbitrary function in the theory, in addition to the usual one due to reparametrization invariance. The usual Newton-Wigner variables are supplemented by the Euler angles. The quantum theory of the free top is discussed. The classical theory is generalized to included charged tops with magnetic moments.     

On the hydrodynamics of Fermi superfluids

The hydrodynamic of a neutral Fermi fluid is derived from the microscopic pairing model in the framework of a time dependent BCS formalism. A discussion of the superfluidity and coherence properties of these fluids and a comparison with the known He II hydrodynamics is attempted. Applications to finite nuclear systems are discussed.     

Role of surface integrals in the Hamiltonian formulation of general relativity

It is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces, the Hamiltonian does not vanish but its value is given rather by a nonzero surface integral. If the deformations of the surface on which the state is defined are restricted so that the surface moves asymptotically parallel to itself in the time direction, then the surface integral gives directly the energy of the system, prior to fixing the coordinates or solving the constraints. Under more general conditions (when asymptotic Poincaré transformations are allowed) the surface integrals giving the total momentum and angular momentum also contribute to the Hamiltonian. These quantities are also identified without reference to a particular fixation of the coordinates. When coordinate conditions are imposed the associated reduced Hamiltonian is unambiguously obtained by introducing the solutions of the constraints into the surface integral giving the numerical value of the unreduced Hamiltonian. In the present treatment there are therefore no divergences that cease to be divergences after coordinate conditions are imposed. The procedure of reduction of the Hamiltonian is explicity carried out for two cases: (a) Maximal slicing, (b) ADM coordinate conditions.A Hamiltonian formalism which is manifestly covariant under Poincaré transformations at infinity is presented. In such a formalism the ten independent variables describing the asymptotic location of the surface are introduced, together with corresponding conjugate momenta, as new canonical variables in the same footing with the g_ij, π^ij. In this context one may fix the coordinates in the “interior” but still leave open the possibility of making asymptotic Poincaré transformations. In that case all ten generators of the Poincaré group are obtained by inserting the solution of the constraints into corresponding surface integrals.