Three-manifold invariants and their relation with the fundamental group

We consider the 3-manifold invariant I(M) which is defined by means of the Chern-Simons quantum field theory and which coincides with the Reshetikhin-Turaev invariant. We present some arguments and numerical results supporting the conjecture that, for nonvanishing I(M), the absolute value | I(M) | only depends on the fundamental group \pi_1 (M) of the manifold M. For lens spaces, the conjecture is proved when the gauge group is SU(2). In the case in which the gauge group is SU(3), we present numerical computations confirming the conjecture.Comment: 22 pages, Latex document, two eps figure

Gravitational helicity interaction

For gravitational deflections of massless particles of given helicity from a classical rotating body, we describe the general relativity corrections to the geometric optics approximation. We compute the corresponding scattering cross sections for neutrinos, photons and gravitons to lowest order in the gravitational coupling constant. We find that the helicity coupling to spacetime geometry modifies the ray deflection formula of the geometric optics, so that rays of different helicity are deflected by different amounts. We also discuss the validity range of the Born approximation.Comment: 16 pages, 1 figure, to be published in Nuclear Physics

Abelian link invariants and homology

We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link -in a generic manifold M- is homologically trivial, the associated observables coincide with the observables of the sphere S^3. Finally we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.Comment: 18 pages, 3 figures; to be published in Journal of Mathematical Physic

Classical Teichmuller theory and (2+1) gravity

We consider classical Teichmuller theory and the geodesic flow on the cotangent bundle of the Teichmuller space. We show that the corresponding orbits provide a canonical description of certain (2+1) gravity systems in which a set of point-like particles evolve in universes with topology S_g x R where S_g is a Riemann surface of genus g >1. We construct an explicit York's slicing presentation of the associated spacetimes, we give an interpretation of the asymptotic states in terms of measured foliations and discuss the structure of the phase spaces

SU(2) and the Kauffman bracket

A direct relationship between the (non-quantum) group SU(2) and the Kauffman bracket in the framework of Chern-Simons theory is explicitly shown.Comment: 5 page

Perturbative BF theory

We consider a superrenormalisable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renormalisation of this model defined in R3 is presented. The structure of the ISU(2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalised traces of ISU(2) holonomies associated with oriented, framed and coloured knots. The perturbative evaluation of the Wilson lines expectation values is investigated and the up-to-third-order contributions to the perturbative expansion of the observables, which correspond to knot invariants, are produced. The general dependence of the knot observables on the framing is worked out

Deligne-Beilinson cohomology and abelian link invariants: torsion case

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants in $SO(3)\simeq\mathbb{R}P^3$, a toy example of 3-manifold with torsion

SciKit-GStat Uncertainty: A software extension to cope with uncertain geostatistical estimates

This study is focused on an extension of a well established geostatistical software to enable one to effectively and interactively cope with uncertainty in geostatistical applications. The extension includes a rich component library, pre-built interfaces and an online application. We discuss the concept of replacing the empirical variogram with its uncertainty bound. This enables one to acknowledge uncertainties characterizing the underlying geostatistical datasets and typical methodological approaches. This allows for a probabilistic description of the variogram and its parameters at the same time. Our approach enables (1) multiple interpretations of a sample and (2) a multi-model context for geostatistical applications. We focus the sample application on propagating observation uncertainties into manual variogram parametrization and analyze its effects. Using two different datasets, we show how insights on uncertainty can be used to reject variogram models, thus constraining the space of formally equally probable models to tackle the issue of parameter equifinality

Gravitational deflection of light and helicity asymmetry

The helicity modification of light polarization which is induced by the gravitational deflection from a classical heavy rotating body, like a star or a planet, is considered. The expression of the helicity asymmetry is derived; this asymmetry signals the gravitationally induced spin transfer from the rotating body to the scattered photons.Comment: 6 pages, 1 figur

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page