235 research outputs found
Super coset space geometry
Super coset spaces play an important role in the formulation of
supersymmetric theories. The aim of this paper is to review and discuss the
geometry of super coset spaces with particular focus on the way the geometrical
structures of the super coset space G/H are inherited from the super Lie group
G. The isometries of the super coset space are discussed and a definition of
Killing supervectors - the supervectors associated with infinitesimal
isometries - is given that can be easily extended to spaces other than coset
spaces.Comment: 49 pages, 1 figure, AFK previously published under the name A. F.
Schunc
Abelian BF theory and Turaev-Viro invariant
The U(1) BF Quantum Field Theory is revisited in the light of
Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition
function is related to the BF one and how the latter on its turn coincides with
an abelian Turaev-Viro invariant. Significant differences compared to the
non-abelian case are highlighted.Comment: 47 pages and 6 figure
Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures
Studying the topological aspects of M-branes in M-theory leads to various
structures related to Wu classes. First we interpret Wu classes themselves as
twisted classes and then define twisted notions of Wu structures. These
generalize many known structures, including Pin^- structures, twisted Spin
structures in the sense of Distler-Freed-Moore, Wu-twisted differential
cocycles appearing in the work of Belov-Moore, as well as ones introduced by
the author, such as twisted Membrane and twisted String^c structures. In
addition, we introduce Wu^c structures, which generalize Pin^c structures, as
well as their twisted versions. We show how these structures generalize and
encode the usual structures defined via Stiefel-Whitney classes.Comment: 20 page
Supermetrics on supermanifolds
By virtue of the well-known theorem, a structure Lie group K of a principal
bundle is reducible to its closed subgroup H iff there exists a global
section of the quotient bundle P/K. In gauge theory, such sections are treated
as Higgs fields, exemplified by pseudo-Riemannian metrics on a base manifold of
P. Under some conditions, this theorem is extended to principal superbundles in
the category of G-supermanifolds. Given a G-supermanifold M and a graded frame
superbundle over M with a structure general linear supergroup, a reduction of
this structure supergroup to an orthgonal-symplectic supersubgroup is
associated to a supermetric on a G-supermanifold M.Comment: 17 page
Model study of the cross-tropopause transport of biomass burning pollution
We present a modeling study of the troposphere-to-stratosphere transport (TST) of pollution from major biomass burning regions to the tropical upper troposphere and lower stratosphere (UT/LS). TST occurs predominately through 1) slow ascent in the tropical tropopause layer (TTL) to the LS and 2) quasi-horizontal exchange to the lowermost stratosphere (LMS). We show that biomass burning pollution regularly and significantly impacts the composition of the TTL, LS, and LMS. Carbon monoxide (CO) in the LS in our simulation and data from the Aura Microwave Limb Sounder (MLS) shows an annual oscillation in its composition that results from the interaction of an annual oscillation in slow ascent from the TTL to the LS and seasonal variations in sources, including a semi-annual oscillation in CO from biomass burning. The impacts of CO sources that peak when ascent is seasonally low are damped (e.g. Southern Hemisphere biomass burning) and vice-versa for sources that peak when ascent is seasonally high (e.g. extra-tropical fossil fuels). Interannual variation of CO in the UT/LS is caused primarily by year-to-year variations in biomass burning and the locations of deep convection. During our study period, 1994–1998, we find that the highest concentrations of CO in the UT/LS occurred during the strong 1997–1998 El Niño event for two reasons: i. tropical deep convection shifted to the eastern Pacific Ocean, closer to South American and African CO sources, and ii. emissions from Indonesian biomass burning were higher. This extreme event can be seen as an upper bound on the impact of biomass burning pollution on the UT/LS. We estimate that the 1997 Indonesian wildfires increased CO in the entire TTL and tropical LS (>60 mb) by more than 40% and 10%, respectively, for several months. Zonal mean ozone increased and the hydroxyl radical decreased by as much as 20%, increasing the lifetimes and, subsequently TST, of trace gases. Our results indicate that the impact of biomass burning pollution on the UT/LS is likely greatest during an El Niño event due to favorable dynamics and historically higher burning rates
Torsion cycles as non-local magnetic sources in non-orientable spaces
Non-orientable spaces can appear to carry net magnetic charge, even in the
absence of magnetic sources. It is shown that this effect can be understood as
a physical manifestation of the existence of torsion cycles of codimension one
in the homology of space.Comment: 17 pages, 4 figure
Gauge theory of Faddeev-Skyrme functionals
We study geometric variational problems for a class of nonlinear sigma-models
in quantum field theory. Mathematically, one needs to minimize an energy
functional on homotopy classes of maps from closed 3-manifolds into compact
homogeneous spaces G/H. The minimizers are known as Hopfions and exhibit
localized knot-like structure. Our main results include proving existence of
Hopfions as finite energy Sobolev maps in each (generalized) homotopy class
when the target space is a symmetric space. For more general spaces we obtain a
weaker result on existence of minimizers in each 2-homotopy class.
Our approach is based on representing maps into G/H by equivalence classes of
flat connections. The equivalence is given by gauge symmetry on pullbacks of
G-->G/H bundles. We work out a gauge calculus for connections under this
symmetry, and use it to eliminate non-compactness from the minimization problem
by fixing the gauge.Comment: 34 pages, no figure
Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators
The theory of geometric phase is generalized to a cyclic evolution of the
eigenspace of an invariant operator with -fold degeneracy.
The corresponding geometric phase is interpreted as a holonomy inherited from
the universal connection of a Stiefel U(N)-bundle over a Grassmann manifold.
Most significantly, for an arbitrary initial state, this geometric phase
captures the inherent geometric feature of the state evolution. Moreover, the
geometric phase in the evolution of the eigenspace of an adiabatic action
operator is also addressed, which is elaborated by a pullback U(N)-bundle.
Several intriguing physical examples are illustrated.Comment: Added Refs. and corrected typos; 4 page
Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape
An estimate is derived for the volume fraction of a subset in the neighborhood
of the critical set
of the kinematic quantum ensemble control landscape J(U) = Tr(U\rho U' O),
where represents the unitary time evolution operator, {\rho} is the initial
density matrix of the ensemble, and O is an observable operator. This estimate
is based on the Hilbert-Schmidt geometry for the unitary group and a
first-order approximation of . An upper bound on these
near-critical volumes is conjectured and supported by numerical simulation,
leading to an asymptotic analysis as the dimension of the quantum system
rises in which the volume fractions of these "near-critical" sets decrease to
zero as increases. This result helps explain the apparent lack of influence
exerted by the many saddles of over the gradient flow.Comment: 27 pages, 1 figur
Completeness of Wilson loop functionals on the moduli space of and -connections
The structure of the moduli spaces \M := \A/\G of (all, not just flat)
and connections on a n-manifold is analysed. For any
topology on the corresponding spaces \A of all connections which satisfies
the weak requirement of compatibility with the affine structure of \A, the
moduli space \M is shown to be non-Hausdorff. It is then shown that the
Wilson loop functionals --i.e., the traces of holonomies of connections around
closed loops-- are complete in the sense that they suffice to separate all
separable points of \M. The methods are general enough to allow the
underlying n-manifold to be topologically non-trivial and for connections to be
defined on non-trivial bundles. The results have implications for canonical
quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-
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