Functional-Integral Approach to Dual-Resonance Theory

It is shown that dual-resonance amplitudes can be expressed in terms of rudimental amplitudes defined by functional integrals which correspond to transition amplitudes of quantum-mechanical systems of strings with imaginary time. The equivalence between the path-integral and operator formulation of quantum mechanics is used to establish the connection between this approach and the usual operator approach. The factorization of rudimental amplitudes is studied to obtain the Feynman-like rules for dual-resonance amplitudes. This allows us to express $N$-Reggeon vertices in terms of rudimental amplitudes, and to determine the propagator, which is shown to be the usual spurious-free twisted propagator. $N$-loop orientable diagrams are calculated. In general, the functional integrals considered can be calculated by solving appropriate Neuman's boundary-value problems of corresponding bounded Riemann surfaces. This provides a generalization of the analog model to the case of external Reggeons which are described by extended momentum distributions on the boundaries.