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

TL;DR

This paper resolves an inconsistency in light cone quantum field theory by demonstrating that the two-point function's restriction to the nullplane is not canonical but a tame restriction, which is independent of mass.

Contribution

The paper introduces the concept of tame restriction for the two-point function and shows it is independent of mass, clarifying a longstanding inconsistency.

Findings

Two-point function has no canonical restriction to the nullplane.

Tame restriction exists and is independent of mass.

Resolves the inconsistency in light cone QFT regarding mass dependence.

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 $\Sigma=\{x^0+x^3=0\}$ 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 $\Sigma$ 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 $\Sigma$.