# Structure of light front vacuum sector diagrams

## TL;DR

This paper investigates the structure of vacuum diagrams in light front quantization of scalar fields, revealing that non-pole contributions cause vacuum diagrams to differ from instant time quantization, challenging the Fock space approach.

## Contribution

It demonstrates that the light front vacuum sector cannot be fully described by the Fock space approach due to circle at infinity contributions in Feynman diagrams.

## Key findings

- Vacuum diagrams in light front quantization include non-pole contributions.
- These contributions make vacuum diagrams nonzero and not describable by Fock space.
- The approach fails in the light front vacuum sector, unlike non-vacuum graphs.

## 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 the 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 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.