[en] We have studied the behaviour of S-matrix poles near the thresholds for some three-body systems. In Amado's simple model for three bosons with an attractive S-wave two-body interaction and spectator angular momentum l = 0, the S-matrix pole behaves as Im E ∝ - (Re E)² near the threshold in the fourth quadrant of the unphysical complex E-plane. This behaviour is formally the same as that in the two-body scattering with angular momentum l = 3/2 and a three-body resonance shows up near the threshold. In such a case, the Fredholm determinant of the Faddeev equation at zero energy, D_F(0), is close to zero. However, it is shown that the value D_F(0) does not definitely tell us whether the system is attractive or repulsive in contrast to the case of a two-body system. As physical applications, we have studied Λnn and Σ^- nn systems. The S-matrix poles are found to be far away from the physical real axis and do not give rise to observable effects for the two-body interactions reproducing the low-energy scattering data, although the Λnn system could develop a three-body resonance if the Λn interaction were slightly more attractive. (orig.)

[en] The low-energy theorem, derived by Terent'ev within the framework of current algebra, is proved at the quark level within the framework of the extended Nambu-Jona-Lasinio (ENJL) model. The γγ→π⁺π^- scattering amplitude was considered at low-energies in the leading order of both chiral and large N experiments. The main tool of the treatment was the constituent-quark-diagram technique developed on the basis of the ENJL-model, especially to prove the soft-pion low-energy theorem at the quark level. (Z.S.) 4 figs., 11 refs

[en] S-matrices for integrable perturbations of N=2 superconformal field theories are studied. The models we consider correspond to perturbations of the coset theory G_kxH_g-h/H_k+g-h. The perturbed models are closely related to G-affine Toda theories with a background charge tuned to H. Using the quantum group restriction of the affine Toda theories we derive the S-matrix. (orig.)

[en] We perform the sewing of two (dual) Ramond reggeon vertices and derive an algorithm by means of which the so obtained four-Ramond reggeon vertex may be explicitly computed at arbitrary oscillator (mass) level. A closed form of the four-vertex is then deduced on the basis of a comparison to all terms obtained by sewing, that contain only level zero and one oscillators. Results are presented for both complex fermions and for the previously studied case of real fermions. (orig.)

[en] This paper reports that the origins of relativistic string theory lie in the dual resonance model of the strong interactions of mesons. The spectrum of hadronic resonances discovered in the 1960's suggested that the mesons might be described as extended relativistic strings with a quark at one end and an antiquark at the other. The quantum states of a relativistic string display the characteristic dependence of spin (J) on mass (M) of string-line Regge pole trajectories, J = α(M²) - n, where n is a non-negative integer and α(s) = α₀ + α's. This is in excellent agreement with observation for most of the meson states on leading (n = 0) Regge trajectories such as the degenerate ρ, ω, f and a₂ trajectories for which α₀ ∼ 0.5 and α' ∼ 1Gev^-1. Furthermore, high-energy two-particle scattering at fixed momentum transfer also fits the Regge pole parametrization, in which the two-particle → two-particle cross section behaves as (-t)^α(s)-1 as t → ∞ with fixed s < 0 where t = -(k₁ + k₄)² and s = -(k₁ + K₂)² are the Mandelstam invariants, K_r^μ are the D-dimensional particle momenta and α(s) = α₀ + α's. More recent data has reinforced this evidence for the string-like structure of the mesons

[en] We derive exact, factorized, purely elastic scattering matrices for the affine Toda theories based on the nonsimply-laced Lie algebras a⁽²⁾_2n-1, b⁽¹⁾_n, c⁽¹⁾_n, d⁽²⁾_n, and g⁽¹⁾₂, as well as the superalgebras A⁽⁴⁾(0, 2n) and B⁽¹⁾(0, n). (orig.)

[en] Starting from the axiomatic field-theory principles (analyticity, unitarity and polynomial boundedness) we obtain high-energy bounds on the amplitude of elastic scattering in a space-time of general dimension D. This is of interest due to recently developed theories in higher dimensions. A comparison of our bounds (which are rigorously valid only for a theory with a mass gap) with the high-energy behaviour of string amplitude, summed up to all loops by Amati, Ciafaloni and Veneziano, shows that O₂Inel saturates our bound, while consistency with the behaviour of σ_tot requires D >> 6 and a fast shrinking of the analyticity ellipse (which might indicate nonlocality of the string theory). This behaviour of σ_tot is due to massless graviton exchange and violates our bounds if no shrinking of the analyticity ellipse is assumed. Our fixed-angle bound, however, is obeyed by the high-energy fixed-angle behaviour of elastic string scattering amplitudes in all orders obtained by Mende and Ooguri. We also show that analyticity of the amplitude in s leads to the well-known extension of the analyticity domain. Alternatives to polynomial boundedness (relevant to string theories) are also discussed. (orig.)

[en] We derive four-dimensional relativistic three-body equations for the case of a field theory with a three-point interaction vertex. These equations describe the coupled 2→2, 2→3, and 3→3 processes, and provide the means of calculating the kernel of the 2→2 Bethe-Salpeter equation. Our equations differ from all previous formulations in two essential ways. Firstly, we have overcome the overcounting problems inherent in earlier works. Secondly, we have retained all possible two-body forces when one particle is a spectator. In this respect, we show how it is necessary to also retain certain three-body forces as these can give rise to (previously overlooked) two-body forces when used in a 2→3 process. The revealing of such hidden two-body forces gives rise to a further novel feature of our equations, namely, to the appearance of a number of subtraction terms. In the case of the πNN system, for example, the NN potential involves a subtraction term where two pions, exchanged between the nucleons, interact with each other through the ππ t-matrix. The necessity of an input ππ interaction is surprising and contrasts markedly with the corresponding three-dimensional description of the πNN system where no such interaction explicitly appears. This illustrates the somewhat unexpected result that the four-dimensional equations differ from the three-dimensional ones even at the operator level. ((orig.))

[en] We obtain a general Euclidean connection for so(n,m). This Euclidean connection allows an algebraic derivation of the S-matrix and it reduces to the known one in appropriate circumstances. Also, we obtain geometric Hamiltonians which are related to this Euclidean connection. The algebraic S-matrix for these Hamiltonians is a rational function in angular momentum. (Author)

[en] The elegant instanton calculus of Lipatov and others used to find factorially divergent behavior (g^NN exclamation point) for N_g much-gt 1 in gφ⁴ perturbation theory is strictly only applicable when all external momenta vanish; a description of high-energy 2→N scattering with N massive particles is beyond the scope of such techniques. On the other hand, a standard multiperipheral treatment of scattering with its emphasis on leading logarithms gives a reasonable picture of high-energy behavior but does not result in factorial divergences. Using a straightforward graphical analysis we present a unified picture of both these phenomena as they occur in the two-particle total cross section of gφ⁴ theory. We do not attempt to tame the unitarity violations associated with either multiperipheralism or the Lipatov technique at strong coupling