MOYAL BRACKETS IN M-THEORY

The infinite limit of matrix theory in four and 10 dimensions is descr ibed in terms of Moyal brackets. In those dimensions there exists a Bo gomol'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 coordinates as nonlocal spinor bilinears, which are generalisations of the standa rd Wigner functions on phase space, is given.