Abstract
An integral-representation is explicitly established for the dual-resonance amplitudes with two off-the-mass-shell states which interact with several unexcited states within the framework of Schwarz's off-shell dual scalar (orbital) theory. The procedure to be employed is based on a functional-integral method and shares its most steps in common with those of the functional method used in the on-shell theory: One crucial difference is the presence of the Carrigan-Fairlie boundary condition. The main ingredients of the formula are compactly written in terms of Jacobi's theta functions which also play a judicious role in other various stages of the present formulation. The representation established is shown to be valid only when the intercept of the leading trajectory is one and the transverse degree of space-time dimensions is twenty-four. It is also demonstrated how our amplitudes reduce to the totally on-shell Bardak'ii-Ruegg amplitudes if both of the two-off-shell particles are put on the ground state shells: We also obtain the amplitudes with one off-shell line in the course.
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