Exchange of coherent particle states and the relativistic eikonal expansion

M. G. Gundzik*, S. Nussinov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A nonpolynomial Lagrangian model for the description of high-energy scattering processes is investigated. The interaction between primary scalar particles corresponding to the operator ψ(x) is mediated by an appropriate coherent state η(x) of secondary scalar particles of mass μ described by the single-particle operator κ(x) with annihilation and creation operators a(k→), a†(k→) satisfying the usual commutation relations. In this picture an effective Lagrangian is introduced with the form LI(x)=G:ψ†(x)η(x)ψ(x):, where η(x)=g(α):exp1(2π) 32dk→2ω[α(k)a†(k→)eik • x+H. c.]-1 with g(α)=exp-121(2π)32dk→2ω|α(k)|2 η(0)+g(α) generates the coherent state for the field case specified by the complex function α(k). The corresponding term of order G in the S-matrix expansion contributes to the high-energy multiparticle vertex. Calculating the propagator for the field η(x), one finds that the contribution to the scattering amplitude due to the single-coherent-state exchange has the form of a generalized relativistic eikonal approximation. This is related to the usual eikonal form (EF) of a particular subset of Feynman diagrams. The corrections to the high-energy EF are viewed as the deviations from pure coherent-state exchange contained in the perturbation expansion for LI. The generalization of this approach to spin is indicated.

Original languageEnglish
Pages (from-to)1866-1872
Number of pages7
JournalPhysical review D
Issue number6
StatePublished - 1971


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