1,000 research outputs found
A Model for Classical Space-time Co-ordinates
Field equations with general covariance are interpreted as equations for a
target space describing physical space time co-ordinates, in terms of an
underlying base space with conformal invariance. These equations admit an
infinite number of inequivalent Lagrangian descriptions. A model for
reparametrisation invariant membranes is obtained by reversing the roles of
base and target space variables in these considerations.Comment: 9 pages, Latex. This was the basis of a talk given at the Argonne
National Laboratory 1996 Summer Institute : Topics on Non-Abelian Duality
June 27-July 1
Wigner Trajectory Characteristics in Phase Space and Field Theory
Exact characteristic trajectories are specified for the time-propagating
Wigner phase-space distribution function. They are especially simple---indeed,
classical---for the quantized simple harmonic oscillator, which serves as the
underpinning of the field theoretic Wigner functional formulation introduced.
Scalar field theory is thus reformulated in terms of distributions in field
phase space. Applications to duality transformations in field theory are
discussed.Comment: 9 pages, LaTex2
Finite Euler Hierarchies And Integrable Universal Equations
Recent work on Euler hierarchies of field theory Lagrangians iteratively
constructed {}from their successive equations of motion is briefly reviewed. On
the one hand, a certain triality structure is described, relating arbitrary
field theories, {\it classical\ts} topological field theories -- whose
classical solutions span topological classes of manifolds -- and
reparametrisation invariant theories -- generalising ordinary string and
membrane theories. On the other hand, {\it finite} Euler hierarchies are
constructed for all three classes of theories. These hierarchies terminate with
{\it universal\ts} equations of motion, probably defining new integrable
systems as they admit an infinity of Lagrangians. Speculations as to the
possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p.,
(Plain TeX), DTP-92/3
Why Matrix theory works for oddly shaped membranes
We give a simple proof of why there is a Matrix theory approximation for a
membrane shaped like an arbitrary Riemann surface. As corollaries, we show that
noncompact membranes cannot be approximated by matrices and that the Poisson
algebra on any compact phase space is U(infinity). The matrix approximation
does not appear to work properly in theories such as IIB string theory or
bosonic membrane theory where there is no conserved 3-form charge to which the
membranes couple.Comment: 8 pages, 4 figures, revtex; references adde
A New Deformation of W-Infinity and Applications to the Two-loop WZNW and Conformal Affine Toda Models
We construct a centerless W-infinity type of algebra in terms of a generator
of a centerless Virasoro algebra and an abelian spin-1 current. This algebra
conventionally emerges in the study of pseudo-differential operators on a
circle or alternatively within KP hierarchy with Watanabe's bracket.
Construction used here is based on a special deformation of the algebra
of area preserving diffeomorphisms of a 2-manifold. We show that
this deformation technique applies to the two-loop WZNW and conformal affine
Toda models, establishing henceforth invariance of these models.Comment: 8 page
Continuous approximation of binomial lattices
A systematic analysis of a continuous version of a binomial lattice,
containing a real parameter and covering the Toda field equation as
, is carried out in the framework of group theory. The
symmetry algebra of the equation is derived. Reductions by one-dimensional and
two-dimensional subalgebras of the symmetry algebra and their corresponding
subgroups, yield notable field equations in lower dimensions whose solutions
allow to find exact solutions to the original equation. Some reduced equations
turn out to be related to potentials of physical interest, such as the
Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like
approximate solution is also obtained which reproduces the Eguchi-Hanson
instanton configuration for . Furthermore, the equation under
consideration is extended to --dimensions. A spherically symmetric form
of this equation, studied by means of the symmetry approach, provides
conformally invariant classes of field equations comprising remarkable special
cases. One of these enables us to establish a connection with the
Euclidean Yang-Mills equations, another appears in the context of Differential
Geometry in relation to the socalled Yamabe problem. All the properties of the
reduced equations are shared by the spherically symmetric generalized field
equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic
BATAL The Balloon Measurement Campaigns of the Asian Tropopause Aerosol Layer
We describe and show results from a series of field campaigns that used balloonborne instruments launched from India and Saudi Arabia during the summers 2014-17 to study the nature, formation, and impacts of the Asian Tropopause Aerosol Layer (ATAL). The campaign goals were to i) characterize the optical, physical, and chemical properties of the ATAL; ii) assess its impacts on water vapor and ozone; and iii) understand the role of convection in its formation. To address these objectives, we launched 68 balloons from four locations, one in Saudi Arabia and three in India, with payload weights ranging from 1.5 to 50 kg. We measured meteorological parameters; ozone; water vapor; and aerosol backscatter, concentration, volatility, and composition in the upper troposphere and lower stratosphere (UTLS) region. We found peaks in aerosol concentrations of up to 25 cm(-3) for radii \u3e 94 nm, associated with a scattering ratio at 940 nm of approximate to 1.9 near the cold-point tropopause. During medium-duration balloon flights near the tropopause, we collected aerosols and found, after offline ion chromatography analysis, the dominant presence of nitrate ions with a concentration of about 100 ng m(-3). Deep convection was found to influence aerosol loadings 1 km above the cold-point tropopause. The Balloon Measurements of the Asian Tropopause Aerosol Layer (BATAL) project will continue for the next 3-4 years, and the results gathered will be used to formulate a future National Aeronautics and Space Administration-Indian Space Research Organisation (NASA-ISRO) airborne campaign with NASA high-altitude aircraft
Sylvester-t' Hooft generators of sl(n) and sl(n|n), and relations between them
Among the simple finite dimensional Lie algebras, only sl(n) possesses two
automorphisms of finite order which have no common nonzero eigenvector with
eigenvalue one. It turns out that these automorphisms are inner and form a pair
of generators that allow one to generate all of sl(n) under bracketing. It
seems that Sylvester was the first to mention these generators, but he used
them as generators of the associative algebra of all n times n matrices Mat(n).
These generators appear in the description of elliptic solutions of the
classical Yang-Baxter equation, orthogonal decompositions of Lie algebras, 't
Hooft's work on confinement operators in QCD, and various other instances. Here
I give an algorithm which both generates sl(n) and explicitly describes a set
of defining relations. For simple (up to center) Lie superalgebras, analogs of
Sylvester generators exist only for sl(n|n). The relations for this case are
also computed.Comment: 14 pages, 6 figure
Features of Time-independent Wigner Functions
The Wigner phase-space distribution function provides the basis for Moyal's
deformation quantization alternative to the more conventional Hilbert space and
path integral quantizations. General features of time-independent Wigner
functions are explored here, including the functional ("star") eigenvalue
equations they satisfy; their projective orthogonality spectral properties;
their Darboux ("supersymmetric") isospectral potential recursions; and their
canonical transformations. These features are illustrated explicitly through
simple solvable potentials: the harmonic oscillator, the linear potential, the
Poeschl-Teller potential, and the Liouville potential.Comment: 18 pages, plain LaTex, References supplemente
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