Perturbation Analyticity and Axiomatic Analyticity. I. Connection of the Landau Singularity Manifold with KällénΞn(t)Manifold and Jost DANAD Manifold

For a class of Feynman graphs ${\mathcal{G}}_n$ (single-loop diagrams with all internal diagonals), the $p$-space perturbation Landau singularity manifolds are shown to be formally of the same structure as the Källén ${\Xi }_n\mathrm{}\left(t\right)\mathrm{}$ manifolds for the $x$-space axiomatic primitive domain. The boundary of the Landau manifold is then shown to be the (DANAD)′ manifold. The relationship between the (DANAD)′ and the Jost (DANAD) manifold is a precise generalization of what exists between the ${F_{\mathrm{kl}}}^{\prime }$ and $F_{\mathrm{kl}}$ surfaces of Källén and Wightman. Since the (DANAD)′ defines a natural domain of holomorphy, the axiomatic envelope of holomorphy cannot be expected to be continuable beyond (DANAD)′. This (DANAD)′ result furnishes a specific conjecture to part of the envelope of holomorphy.