Lagrangian quantum field theory in momentum picture. III. Free vector fields

TL;DR

This paper analyzes free vector quantum fields in the momentum picture, deriving their equations, commutation relations, and discussing vacuum states, with special focus on massless fields like electromagnetism.

Contribution

It provides a detailed formulation of free vector fields in the momentum picture, including derivation of commutation relations and analysis of massless cases such as electromagnetism.

Findings

Derived field equations in terms of creation and annihilation operators

Discussed vacuum and state vector issues for free vector fields

Explored peculiarities of massless vector fields like electromagnetism

Abstract

Free vector fields, satisfying the Lorenz condition, are investigated in details in the momentum picture of motion in Lagrangian quantum field theory. The field equations are equivalently written in terms of creation and annihilation operators and on their base the commutation relations are derived. Some problems concerning the vacuum and state vectors of free vector field are discussed. Special attention is paid to peculiarities of the massless case; in particular, the electromagnetic field is explored. Several Lagrangians, describing free vector fields, are considered and the basic consequences of them are pointed and compared.