1,721,049 research outputs found
Harmonic forms and spinors on the Taub-bolt space
Full text linkThis paper studies the space of L2 harmonic forms and L2 harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L2 zero modes of D̸ A , the Dirac operator twisted by an arbitrary L2 harmonic connection A, and independently compute the index of D̸ A . We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild
Valse poco a poco [music] : for piano solo /
No full textCover title.; "Played with great success by Mark Hambourg" -- Cover.; Also available online http://nla.gov.au/nla.mus-an4811504.Poco a poc
Valse Poco a poco [music] : for piano /
No full textCover title.; Poco a poco--Caption title.; "M. Hambourg".; Geo. Murray & Co. Ltd. Lithographers Sydney.; Also available online http://nla.gov.au/nla.mus-an22986337.Poco a poc
Adiabatic Dynamics of Instantons on S4
Full text linkWe define and compute the L2 metric on the framed moduli space of circle invariant 1-instantons on the 4-sphere. This moduli space is four dimensional and our metric is SO(3)×U(1) symmetric. We study the behaviour of generic geodesics and show that the metric is geodesically incomplete. Circle-invariant instantons on the 4-sphere can also be viewed as hyperbolic monopoles, and we interpret our results from this viewpoint. We relate our results to work by Habermann on unframed instantons on the 4-sphere and, in the limit where the radius of the 4-sphere tends to infinity, to results on instantons on Euclidean 4-space
Gravitational instantons as models for charged particle systems
No full textIn this paper we propose ALF gravitational instantons of types A(k) and D-k as models for charged particle systems. We calculate the charges of the two families. These are -(k + 1) for Ak, which is proposed as a model for k + 1 electrons, and 2 - k for D-k, which is proposed as a model for either a particle of charge +2 and k electrons or a proton and k + 1 electrons. Making use of preferred topological and metrical structures of the manifolds, namely metrically preferred representatives of middle dimension homology classes, we construct two different energy functionals which reproduce the Coulomb interaction energy for a system of charged particles
Harmonic forms on ALF gravitational instantons
Full text linkAbstract: We study the space of square-integrable harmonic forms over ALF gravitational instantons of type AK−1 and of type DK. We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the Hodge cohomology of a gravitational instanton M to the singular cohomology of a particular compactification XM of M. We then exhibit an explicit basis, exact for AK−1 and approximate for DK, and interpret geometrically the relations between M, XM and their cohomologies.</p
Harmonic spinors on a family of Einstein manifolds
Full text linkThe purpose of this paper is to study harmonic spinors defined on a 1-parameter family of Einstein manifolds which includes Taub–NUT, Eguchi–Hanson and P2(C) with the Fubini–Study metric as particular cases. We discuss the existence of and explicitly solve for spinors harmonic with respect to the Dirac operator twisted by a geometrically preferred connection. The metrics examined are defined, for generic values of the parameter, on a non-compact manifold with the topology of C2 and extend to P2(C) as edge-cone metrics. As a consequence, the subtle boundary conditions of the Atiyah–Patodi–Singer index theorem need to be carefully considered in order to show agreement between the index of the twisted Dirac operator and the result obtained by counting the explicit solutio
Kaluza-Klein reductions of maximally supersymmetric five-dimensional lorentzian spacetimes
Full text linkA recent study of filtered deformations of (graded subalgebras of) the minimal five-dimensional Poincaré superalgebra resulted in two classes of maximally supersymmetric spacetimes. One class are the well-known maximally supersymmetric backgrounds of minimal five-dimensional supergravity, whereas the other class does not seem to be related to supergravity. This paper is a study of the Kaluza–Klein (KK) reductions to four dimensions of this latter class of maximally supersymmetric spacetimes. We classify the Lorentzian and Riemannian KK reductions of these backgrounds, determine the fraction of the supersymmetry preserved under the reduction and in most cases determine explicitly the geometry of the four-dimensional quotient. Among the many supersymmetric quotients found, we highlight a number of novel non-homogeneous four-dimensional Lorentzian spacetimes admitting N = 1 supersymmetry, whose supersymmetry algebra is not a filtered deformation of any graded subalgebra of the four-dimensional N = 1 Poincaré superalgebra. Any of these four-dimensional Lorentzian spacetimes may serve as the arena for the construction of new rigidly supersymmetric field theories
Poco a poco [music]: valse for piano /
No full textCatalogue record generated as part of a batch load; "Played with great success by Mark Hambourg".; Second edition.; Also available online http://nla.gov.au/nla.mus-vn5715920
Time evolution in a geometric model of a particle
Full text linkWe analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac’s Large Number Hypothesis
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