The Light-Front Vacuum

TL;DR

This paper investigates the relationship between the trivial vacuum in light-front quantum field theory and the non-trivial vacuum in canonical formulations, revealing a unitary mapping that preserves locality and Poincaré invariance.

Contribution

It demonstrates how the light-front vacuum can be extended to local observables, establishing a unitary correspondence with the canonical vacuum and clarifying the role of zero-modes.

Findings

The vacuum functional extends from light-front to local algebra.

A unitary mapping relates the light-front and canonical vacua.

The approach preserves locality and Poincaré invariance.

Abstract

Background: The vacuum in the light-front representation of quantum field theory is trivial while vacuum in the equivalent canonical representation of the same theory is non-trivial. Purpose: Understand the relation between the vacuum in light-front and canonical representations of quantum field theory and the role of zero-modes in this relation. Method: Vacuua are defined as linear functionals on an algebra of field operators. The role of the algebra in the definition of the vacuum is exploited to understand this relation. Results: The vacuum functional can be extended from the light-front Fock algebra to an algebra of local observables. The extension to the algebra of local observables is responsible for the inequivalence. The extension defines a unitary mapping between the physical representation of the local algebra and a sub-algebra of the light-front Fock algebra. Conclusion: There is a unitary mapping from the physical representation of the algebra of local observables to a sub-algebra of the light-front Fock algebra with the free light-front Fock vacuum. The dynamics appears in the mapping and the structure of the sub-algebra. This correspondence provides a formulation of locality and Poincar\'e invariance on the light-front Fock space.