774 research outputs found

### Implicit Solutions of PDE's

Further investigations of implicit solutions to non-linear partial
differential equations are pursued. Of particular interest are the equations
which are Lorentz invariant. The question of which differential equations of
second order for a single unknown $\phi$ are solved by the imposition of an
inhomogeneous quadratic relationship among the independent variables, whose
coefficients are functions of $\phi$ is discussed, and it is shown that if the
discriminant of the quadratic vanishes, then an implicit solution of the
so-called Universal Field Equation is obtained. The relation to the general
solution is discussed.Comment: 11 pages LaTeX2

### Study of Quommutators of Quantum Variables and Generalized Derivatives

A general deformation of the Heisenberg algebra is introduced with two
deformed operators instead of just one. This is generalised to many variables,
and permits the simultaneous existence of coherent states, and the
transposition of creation operators.Comment: 17 pages (Previous version was truncated in transmission

### Moyal Brackets in M-Theory

The infinite limit of Matrix Theory in 4 and 10 dimensions is described in
terms of Moyal Brackets. In those dimensions there exists a Bogomol'nyi bound
to the Euclideanized version of these equations, which guarantees that
solutions of the first order equations also solve the second order Matrix
Theory equations. A general construction of such solutions in terms of a
representation of the target space co-ordinates as non-local spinor bilinears,
which are generalisations of the standard Wigner functions on phase space, is
given.Comment: 10 pages, Latex, no figures. References altered, typos correcte

### Integrable Top Equations associated with Projective Geometry over Z_2

We give a series of integrable top equations associated with the projective
geometry over Z_2 as a (2^n-1)-dimensional generalisation of the 3D Euler top
equations. The general solution of the (2^n-1)D top is shown to be given by an
integration over a Riemann surface with genus (2^{n-1}-1)^2.Comment: 8 pages, Late

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