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- W1979408515 abstract "It is shown that the imaginary part of the scattering amplitude A1(t,s) is positive and has all positive derivatives with respect to the momentum transfer t in the non-physical region up to its first singularity given by the Landau curve t = t1(s). Hence for the Regge pole with largest l we have dl/dt > 0 in this interval. The dependence of l on t is studied when t → 4μ2. It appears that l(t) = R(t)+const · (4μ2−t)λ+12ifλ+12 is not an integer, and l(t) = R1(t)+const · (t−4μ2)λ+1 ln(4μ2−t) if it is; λ = l(4μ2), and the functions R and R1 have no singularity when t → 4μ2. It is proved that l(t) goes into the upper half-plane when t>4μ2. All these results are obtained without the assumption of the existence of a Hamiltonian. Different possibilities are discussed for the dependence l(t) when t→∞. It is analysed whether the poles corresponding to the “elementary particles” are continuous functions of l. In the Appendix it is shown that in calculating the spectral density π(s,t) the conditions s(t−4μ2) < μ4 is the condition of neglecting all singularities in the l plane except the pole with the maximum Re l." @default.
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- W1979408515 date "1962-10-01" @default.
- W1979408515 modified "2023-10-16" @default.
- W1979408515 title "Properties of the elastic scattering amplitude at high energies" @default.
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- W1979408515 doi "https://doi.org/10.1016/0029-5582(62)91062-3" @default.
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