691 research outputs found
Linearisation of Universal Field Equations
The Universal Field Equations, recently constructed as examples of higher
dimensional dynamical systems which admit an infinity of inequivalent
Lagrangians are shown to be linearised by a Legendre transformation. This
establishes the conjecture that these equations describe integrable systems.
While this construction is implicit in general, there exists a large class of
solutions for which an explicit form may be written.Comment: 11pp., DTP-92/47, NI-92/01
Integrable Generalisations of the 2-dimensional Born Infeld Equation
The Born-Infeld equation in two dimensions is generalised to higher
dimensions whilst retaining Lorentz Invariance and complete integrability. This
generalisation retains homogeneity in second derivatives of the field.Comment: 11 pages, Latex, DTP/93/3
Impact of multiscale dynamical processes and mixing on the chemical composition of the upper troposphere and lower stratosphere during the Intercontinental Chemical Transport Experiment–North America
We use high-frequency in situ observations made from the DC8 to examine fine-scale tracer structure and correlations observed in the upper troposphere and lower stratosphere during INTEX-NA. Two flights of the NASA DC-8 are compared and contrasted. Chemical data from the DC-8 flight on 18 July show evidence for interleaving and mixing of polluted and stratospheric air masses in the vicinity of the subtropical jet in the upper troposphere, while on 2 August the DC-8 flew through a polluted upper troposphere and a lowermost stratosphere that showed evidence of an intrusion of polluted air. We compare data from both flights with RAQMS 3-D global meteorological and chemical model fields to establish dynamical context and to diagnose processes regulating the degree of mixing on each day. We also use trajectory mapping of the model fields to show that filamentary structure due to upstream strain deformation contributes to tracer variability observed in the upper troposphere. An Eulerian measure of strain versus rotation in the large-scale flow is found useful in predicting filamentary structure in the vicinity of the jet. Higher-frequency (6–24 km) tracer variability is attributed to buoyancy wave oscillations in the vicinity of the jet, whose turbulent dissipation leads to efficient mixing across tracer gradients
The Moyal bracket and the dispersionless limit of the KP hierarchy
A new Lax equation is introduced for the KP hierarchy which avoids the use of
pseudo-differential operators, as used in the Sato approach. This Lax equation
is closer to that used in the study of the dispersionless KP hierarchy, and is
obtained by replacing the Poisson bracket with the Moyal bracket. The
dispersionless limit, underwhich the Moyal bracket collapses to the Poisson
bracket, is particularly simple.Comment: 9 pages, LaTe
Anyons as quon particles
The momentum operator representation of nonrelativistic anyons is developed
in the Chern - Simons formulation of fractional statistics. The connection
between anyons and the q-deformed bosonic algebra is established.Comment: 10 pages,Late
q-Ultraspherical polynomials for q a root of unity
Properties of the -ultraspherical polynomials for being a primitive
root of unity are derived using a formalism of the algebra. The
orthogonality condition for these polynomials provides a new class of
trigonometric identities representing discrete finite-dimensional analogs of
-beta integrals of Ramanujan.Comment: 7 pages, LATE
Auxiliary Fields for Super Yang-Mills from Division Algebras
Division algebras are used to explain the existence and symmetries of various
sets of auxiliary fields for super Yang-Mills in dimensions .
(Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)Comment: 7 pages, plain TeX, CERN-TH.7470/9
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
Octonionic representations of Clifford algebras and triality
The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page
Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras
We formulate a theory of generalized Fock spaces which underlies the
different forms of quantum statistics such as ``infinite'', Bose-Einstein and
Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems
that cannot be mapped into single-indexed systems are studied. Our theory is
based on a three-tiered structure consisting of Fock space, statistics and
algebra. This general formalism not only unifies the various forms of
statistics and algebras, but also allows us to construct many new forms of
quantum statistics as well as many algebras of creation and destruction
operators. Some of these are : new algebras for infinite statistics,
q-statistics and its many avatars, a consistent algebra for fractional
statistics, null statistics or statistics of frozen order, ``doubly-infinite''
statistics, many representations of orthostatistics, Hubbard statistics and its
variations.Comment: This is a revised version of the earlier preprint: mp_arc 94-43.
Published versio
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