Structure of light-front vacuum sector diagrams

Abstract

We study the structure of scalar field light-front quantization vacuum graphs. In instant-time quantization both non-vacuum and vacuum graphs can equivalently be described by either the off-shell four-dimensional Feynman diagram approach or the on-shell three-dimensional Fock space approach, with this being the case since the relevant Feynman diagrams are given entirely by pole terms. This is also the case for light-front quantization non-vacuum graphs. However this is not the case for light-front vacuum sector diagrams, since then there are also circle at infinity contributions to Feynman diagrams. These non-pole contributions cause light-front vacuum diagrams to be nonzero and to not be given by a light-front Hamiltonian Fock space analysis. The three-dimensional approach thus fails in the light-front vacuum sector. In consequence, the closely related infinite momentum frame approach also fails in the light-front vacuum sector.