Use of the Generalized Jost Function in Quantum Field Theory : An extension of the Levinson theorem

概要

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The structures of S-matrix are investigated in terms of the so-called generalized Jost function. Starting from the partial wave dispersion relation, we can derive the analytic properties of this function in the single-channel scattering and it is shown that there exists a close connection between the analyticity of this function and the generalized Levinson relation. In the case where the one-particle singularity in scattering amplitudes is due to the elementary particle, the corresponding Jost function has a pole, while in the case where this singularity is due to the composite (bound) state, the Jost function does not have the pole. Singularities corresponding to the Castillejo-Dalitz-Dyson ambiguity are completely separated. Thus, by making the conjecture that these analyticity in the low-momentum region still remains in the multichannel case, we can extend the Levinson theorem to the multichannel case and to the S-matrix theory where the Hamiltonian is not used explicitly. We shall also derive the new representation of S-matrix and how the structure of S-matrix changes according to each case mentioned above will be clarified.
理論物理学刊行会の論文
1963-01-25