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- W2259944377 abstract "The relativistic two-body scattering amplitude is analysed in terms of irreducible representations of the Poincaré group, which describe «objects» exchanged in the scattering process. These representations are obtained by the decomposition of the direct product of the representations, which describe an incoming and an outgoing particle, respectively. This procedure, which uses only the invariance and unitarity properties of the amplitude, is analogous to the usual partial-wave expansion, and we call it «crossed partial-wave analysis». Complex angular momentum appears as a quantum number describing the «exchanged objects». If the TCP invariance is taken into account, also the signature can be introduced in a natural way. The difficulties due to the fact that the representations considered are infinite-dimensional are discussed in detail. It is proved that the crossed partial-wave analysis can be performed for every invariant amplitude which satisfies the unitarity condition. However, the «crossed partial-wave amplitude» has to be considered as a bounded linear functional in a normed space of functions which depend on the quantum numbers which describe the «exchanged objects». Particles with arbitrary spins and parities are considered. The symmetry with respect to time and space inversions, and with respect to the exchange of identical particles, is taken into account. The role of the internal symmetry group is briefly discussed." @default.
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- W2259944377 date "1968-03-01" @default.
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- W2259944377 title "On the group-theoretical approach to complex angular momentum and signature" @default.
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- W2259944377 doi "https://doi.org/10.1007/bf02743789" @default.
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