Multiperipheral scattering and singular Bethe-Salpeter equations

The restrictions of self-consistency are investigated for two sets of interacting particles-vector and scalar (or pseudoscalar)-with unequal masses. Self-consistency is studied within a field-theoretic framework and within a bootstrap framework. It is assumed that solutions exist when the particles of a given set have equal masses and the coupling constants are proportional to the structure constants of SU S . The unequalmass case is studied by perturbing the equal-mass solutions and retaining only first-order terms in the mass and coupling-constant shifts. It is found that fully self-consistent solutions do not exist in either case, but it it is seen how such solutions can come about in the field-theoretic case. In the bootstrap analysis it is very difficult to understand how self-consistent solutions develop unless hidden identities are satisfied.

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“…The coupling constants are taken as proportional to the structure constants of SU Z and Eqs. (10), (11), and (12) of Sec. II are still valid.…”

Section: S-so R P( Fl D)(i');w;w)mentioning

confidence: 96%

Self-Consistent, Nondegenerate Multiplets

Cook

Paton

1965

Phys. Rev.

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“…type) the behavior of the kernels at large momenta does not allow Fredholm expansions. Accordingly, as it is indicated by simple model calculations, 6 ' 8 ' [28][29][30] singularities of anew kind may arise, e.g., square-root branch points in the coupling constant whose direct physical interpretation is not clear. (The analogy!of this situation to the nonrelativistic problem with a potential having an 1/V 2 singularity at the origin is familiar.)…”

Section: D=jr\ns N ( S )mentioning

confidence: 99%

Euclidean Approach to the Bethe-Salpeter Equation for Scattering

Tiktopoulos

1964

Phys. Rev.

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It is shown that the mass-shell scattering amplitude in the physical scattering region (two-particle branch cut) can be directly obtained from the resolvent of the Bethe-Salpeter kernel transformed according to Wick (rotation of the energy integration paths to the imaginary axis). As an illustration and under the assumption that the kernel is approximated by any finite set of irreducible graphs, the scattering amplitude in 4> z theory is given in terms of a Fredholm formula whose convergence is explicitly demonstrated.

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