4,978 research outputs found
Spin Foam Models of Matter Coupled to Gravity
We construct a class of spin foam models describing matter coupled to
gravity, such that the gravitational sector is described by the unitary
irreducible representations of the appropriate symmetry group, while the matter
sector is described by the finite-dimensional irreducible representations of
that group. The corresponding spin foam amplitudes in the four-dimensional
gravity case are expressed in terms of the spin network amplitudes for
pentagrams with additional external and internal matter edges. We also give a
quantum field theory formulation of the model, where the matter degrees of
freedom are described by spin network fields carrying the indices from the
appropriate group representation. In the non-topological Lorentzian gravity
case, we argue that the matter representations should be appropriate SO(3) or
SO(2) representations contained in a given Lorentz matter representation,
depending on whether one wants to describe a massive or a massless matter
field. The corresponding spin network amplitudes are given as multiple
integrals of propagators which are matrix spherical functions.Comment: 30 pages, 9 figures, further remarks and references added. Version to
appear in Class. Quant. Gra
4-Dimensional BF Theory as a Topological Quantum Field Theory
Starting from a Lie group G whose Lie algebra is equipped with an invariant
nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory
with cosmological term gives rise to a TQFT satisfying a generalization of
Atiyah's axioms to manifolds equipped with principal G-bundle. The case G =
GL(4,R) is especially interesting because every 4-manifold is then naturally
equipped with a principal G-bundle, namely its frame bundle. In this case, the
partition function of a compact oriented 4-manifold is the exponential of its
signature, and the resulting TQFT is isomorphic to that constructed by Crane
and Yetter using a state sum model, or by Broda using a surgery presentation of
4-manifolds.Comment: 15 pages in LaTe
Pilot study and evaluation of a SMMR-derived sea ice data base
Data derived from the Nimbus 7 scanning multichannel microwave radiometer (SMMR) are discussed and the types of problems users have with satellite data are documented. The development of software for assessing the SMMR data is mentioned. Two case studies were conducted to verify the SMMR-derived sea ice concentrations and multi-year ice fractions. The results of a survey of potential users of SMMR data are presented, along with SMMR-derived sea ice concentration and multiyear ice fraction maps. The interaction of the Arctic atmosphere with the ice was studied using the Nimbus 7 SMMR. In addition, the characteristics of ice in the Arctic ocean were determined from SMMR data
Cosmological Constant in LQG Vertex Amplitude
A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by
using the evaluation of the Vassiliev invariant associated with a 4-simplex
graph (related to two copies of quantum SU(2) group at different roots of
unity) embedded in a 3-sphere. We show that the large-j asymptotics of the
q-deformed vertex amplitude gives the Regge action with a cosmological
constant. In the end we also discuss its relation with a Chern-Simons theory on
the boundary of 4-simplex.Comment: 6 pages, 5 figures, result and presentation improve
Invariants from classical field theory
We introduce a method that generates invariant functions from perturbative
classical field theories depending on external parameters. Applying our methods
to several field theories such as abelian BF, Chern-Simons and 2-dimensional
Yang-Mills theory, we obtain, respectively, the linking number for embedded
submanifolds in compact varieties, the Gauss' and the second Milnor's invariant
for links in S^3, and invariants under area-preserving diffeomorphisms for
configurations of immersed planar curves.Comment: 20 pages, 1 figure, to appear in J. Math. Phy
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