Time Evolution in String Field Theory and T-duality

The time evolution operator (Schr"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1\mathrm{/}{Z}_2$. We give a graphical derivation of this that generalises to second quantised string theory. T-duality then relates evolution through time t with evolution through 1/t and an interchange of string fields and backgrounds.