Abstract
Scalar meson fields are studied for the conformally flat metric e+ψ(dx12+dx22+dx32 −dx42). Complete sets of solutions of the field equations have been obtained for massless mesons, and the field equations have been reduced to a single ordinary differential equation in ψ for massive mesons. In either case ψ is found to be a function of x12+x22+x32−x42 or c1x1+c2x2+c3x3+c4x4 (c1,c2,c3,c4 being constants), and φ the meson field is found to be constant or a function of ψ.

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