Abstract
The light-front (LF) quantization is applied for the model of massive scalar field with self-interaction. We check some of the LF postulates by considering the Wightman function for this model. The scale symmetry imposed only on the LF quantization hypersurface and the Lorentz symmetry assumed for all points in Minkowski’s space-time lead to a strong constraint for the Wightman functions, which is satisfied only by a free and massless scalar field. This result agrees with the recent Weinberg’s result for a scale-symmetric theory. This means that one cannot expect the unitary equivalence of the Fock space for scalar fields with different masses at the LF hypersurface.
Highlights
In this paper we analyze the consistency and consequences of some postulates which are commonly accepted within the standard LF formulation
Third postulate—the fields with different masses are unitarily equivalent at the LF hypersurface, after [1] a null plane field theory is dilatation invariant in the null plane even if it has a mass, where a null plane is a synonym of a light-front
While Weinberg discusses fields with arbitrary spin, we consider here only a scalar field case. Another difference is that we assume the scaling symmetry only at the LF hypersurface, while Weinberg imposes it for all points in Minkowski’s space-time
Summary
In this paper we analyze the consistency and consequences of some postulates which are commonly accepted within the standard LF formulation. For this aim we consider the vacuum correlation function 0|φ(x) φ(y)|0 , which we will refer to as the 2-point Wightman function. This allows us to work mostly with the c-numbered (generalized) functions instead of the quantum field operators. Second postulate—at the LF hypersurface x+ = 0 the maximal number (7 out of 10) of the Poincaré generators are kinematical: P+, Pi , J+−, J−i , Ji j. Third postulate—the fields with different masses are unitarily equivalent at the LF hypersurface, after [1] a null plane field theory is dilatation invariant in the null plane even if it has a mass, where a null plane is a synonym of a light-front
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