Towards a kinetic theory of strings

We study the dynamics of strings by means of a distribution function f(A,B,x,t), defined on a 9+1D phase space, where A and B are the correlation vectors of right- and left-moving waves. We derive a transport equation (analogous to a Boltzmann transport equation for particles) that governs the evolution of long strings with Nambu-Goto dynamics, as well as reconnections taken into account. We also derive a system of coupled transport equations (analogous to a Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for particles) which can simultaneously describe long strings f(A,B,x,t) as well as simple loops f(A,B,x,t) made out of four correlation vectors. The formalism can be used to study nonlinear dynamics of fundamental strings, D-brane strings, or field theory strings. For example, the complicated semiscaling behavior of cosmic strings translates into a simple solution of the transport system at small energy densities.