17 research outputs found
On the Fairlie's Moyal formulation of M(atrix)- theory
Starting from the Moyal formulation of M-theory in the large N-limit, we
propose to reexamine the associated membrane equations of motion in 10
dimensions formulated in terms of Poisson bracket. Among the results obtained,
we rewrite the coupled first order Nahm's equations into a simple form leading
in turn to their systematic relation with Yang Mills equations of
motion. The former are interpreted as the vanishing condition of some conserved
currents which we propose. We develop also an algebraic analysis in which an
ansatz is considered and find an explicit form for the membrane solution of our
problem. Typical solutions known in literature can also emerge as special cases
of the proposed solutionComment: 16 page
On the harmonic superspace language adapted to the Gelfand-Dickey algebra of differential operators
Methods developed for the analysis of non-linear integrable models are used
in the harmonic superspace (HS) framework. These methods, when applied to the
HS, can lead to extract more information about the meaning of integrability in
non-linear physical problems. Among the results obtained, we give the basic
ingredients towards building in the HS language the analogue of the G.D.
algebra of pseudo-differential operators. Some useful convention notations and
algebraic structures are also introduced to make the use of the harmonic
superspace techniques more accessible.Comment: 14 page