The purpose of this work is to understand the relation between the trivial vacuum in light-front field theory and the nontrivial vacuum in canonical representations of quantum field theory and the role of zero-modes in this relation. The role of the underlying field algebra in the definition of the vacuum is exploited to understand these relations. The trivial vacuum defined by an annihilation operator defines a linear functional on the algebra of fields restricted to a light front. This is extended to a linear functional on the algebra of local fields. The extension defines a unitary mapping between the physical representation of the local algebra and a sub-algebra of the light-front Fock algebra. The dynamics appears in the mapping and the structure of the sub-algebra. This correspondence provides a formulation of locality and Poincaré invariance on the light-front Fock space. Zero modes do not appear in the final mapping, but may be needed in the construction of the mapping using a local Lagrangian.

• Received 10 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.085043