Quantum strings and the functional calculus

The field theory of strings is developed using the functional calculus as a practical technique. A Schr\"odinger-type equation and its eigensolutions are derived in light-cone coordinates. Vertices and amplitudes are represented entirely in a Fock space of second-quantized functionals. Two different open-string interactions are explicitly investigated. The three- and four-string vertex functionals are calculated for arbitrary times and compared with the asymptotic expressions obtained by other authors. We discuss how more exotic string configurations can be incorporated into the theory and emphasize the utility of the functional calculus in describing these topologies.