  A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a
category equipped with structures analogous those of a Lie algebra, for which
the usual laws hold up to isomorphism. In the classical mechanics of point
particles, the phase space is often a symplectic manifold, and the Poisson
bracket of functions on this space gives a Lie algebra of observables.
Multisymplectic geometry describes an n-dimensional field theory using a phase
space that is an "n-plectic manifold": a finite-dimensional manifold equipped
with a closed nondegenerate (n+1)-form. Here we consider the case n = 2. For
any 2-plectic manifold, we construct a Lie 2-algebra of observables. We then
explain how this Lie 2-algebra can be used to describe the dynamics of a
classical bosonic string. Just as the presence of an electromagnetic field
affects the symplectic structure for a charged point particle, the presence of
a B field affects the 2-plectic structure for the string.
