## Categorified symplectic geometry and the classical string (2008)

Citations: | 10 - 5 self |

### BibTeX

@MISC{Baez08categorifiedsymplectic,

author = {John C. Baez and Alexander E. Hoffnung and Christopher L. Rogers},

title = {Categorified symplectic geometry and the classical string},

year = {2008}

}

### OpenURL

### Abstract

A Lie 2-algebra is a ‘categorified ’ version of a Lie algebra: that is, a category equipped with structures analogous to 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.