Role of the Fundamental Tachyon Field in the Elastic Scattering Amplitude

Abstract

In previous papers a fundamental field ${\ensuremath{\varphi}}_{\ensuremath{\alpha}}(x)$ was determined giving a nonperturbative solution of a nonlinear field equation of motion. In one work it was shown how the observable scattering processes corresponding to the fundamental field could be determined in general by applying unitarity to the function ${\ensuremath{\Delta}}_{\ensuremath{\alpha}\ensuremath{\beta}}^{+}(x\ensuremath{-}y)=〈0|{\ensuremath{\varphi}}_{\ensuremath{\alpha}}(x){\ensuremath{\varphi}}_{\ensuremath{\beta}}^{\ifmmode\dagger\else\textdagger\fi{}}(y)|0〉$. In particular the contribution of the fundamental field components with positive mass-squared values to the direct channel of the elastic scattering amplitude was determined. In the present paper it is shown how the contribution of the fundamental tachyon field component (with negative mass-squared values) to the momentum-transfer channel of the elastic scattering amplitude may be determined.