The Poincaré group is represented taking as a complete set of commuting observables {PT,K3,𝒯3}, where K3 is the boost along the third axis and 𝒯3 the third component of the null plane spin. We name it K3‐representation. There appears in it a parameter K, with dimensions of momentum, from which the infinite momentum limit can be implemented in a natural way as the contraction k→∞. K3‐states and wavefunctions are well defined in the infinite momentum limit. They are related to null plane states and wavefunctions by a Mellin transformation. The convergence properties of null plane functions translate into analyticity properties of K3‐functions in the complex λ (eigenvalue of K3)‐plane.

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To be precise, this is only true if the functions o/(P+) satisfy a slightly stronger condition than (21a), namely that they should decrease at P+ = ∞ at least as P+−ε and vanish at P+ =  at least as P+ε for some ε>0. For example, a behavior of o/(p+) like 1/logp+ is enough for (21a) at ∞ but it is not sufficient to guarantee the existence of the analyticity band (21b).
15.
Similar considerations as in (14) apply also here.
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1981
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