particular result that potentials are the better approach in the description of that radiation. A similar problem arises when it is concluded that the dipole approximation amounts to the replacement of the transverse field of a laser by the more elementary longitudinal field. In each of the phrases demarcated by quotation marks, the word field is used in a generic sense to identify an electromagnetic phenomenon.

Constant electric field
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The problem of a particle of mass $m$ and charge $q$ immersed in a constant electric field of magnitude $E_{0}$ is inherently one-dimensional. For present purposes, nothing is gained by going to three spatial dimensions. The problem is clearly one in which energy is conserved. By Noether’s Theorem [@noether], the Lagrangian must be independent of time $t$, so that the connection between the electric field and potentials given in Eq. (\[a\]) must depend only on the scalar potential $\phi.$ Equation (\[a\]) can then be integrated to give the potentials$$\phi=-xE_{0},\qquad A=0, \label{o}$$ since an additive constant of integration has no physical meaning. The potentials descriptive of this problem are unique, and given by Eq. (\[o\]).

The Lagrangian function is the difference of the kinetic energy $T$ and the potential energy $U$:$$\begin{aligned}
