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On the problem of mass-dependence of the two-point function of the real scalar free massive field on the light cone

P. Ullrich·E. Werner
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Abstract

We investigate the generally assumed inconsistency in light cone quantum field theory that the restriction of a massive, real, scalar, free field to the nullplane $Σ=\{x^0+x^3=0\}$ is independent of mass \cite{LKS}, but the restriction of the two-point function depends on it (see, e.g., \cite{NakYam77, Yam97}). We resolve this inconsistency by showing that the two-point function has no canonical restriction to $Σ$ in the sense of distribution theory. Only the so-called tame restriction of the two-point function exists which we have introduced in \cite{Ull04sub}. Furthermore, we show that this tame restriction is indeed independent of mass. Hence the inconsistency appears only by the erroneous assumption that the two-point function would have a (canonical) restriction to $Σ$.

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P. Ullrich, E. Werner. 2005-03-23. On the problem of mass-dependence of the two-point function of the real scalar free massive field on the light cone. https://doi.org/10.1088/0305-4470%2F39%2F20%2F029

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