Editing Scale invariance (section)

===Classical electromagnetism===

An example of a scale-invariant classical field theory is [[electromagnetic field|electromagnetism]] with no charges or currents. The fields are the electric and magnetic fields, '''E'''('''x''',''t'') and '''B'''('''x''',''t''), while their field equations are [[Maxwell's equations]].

With no charges or currents, [[electromagnetic field#Light as an electromagnetic disturbance|these field equations]] take the form of [[wave equation]]s
: <math>
\begin{align}
\nabla^2 \mathbf{E} = \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} \\[6pt]
\nabla^2\mathbf{B} = \frac{1}{c^2} \frac{\partial^2 \mathbf{B}}{\partial t^2}
\end{align}
</math>
where ''c'' is the speed of light.

These field equations are invariant under the transformation
:<math>
\begin{align}
x\rightarrow\lambda x, \\[6pt]
t\rightarrow\lambda t.
\end{align}
</math>

Moreover, given solutions of Maxwell's equations, '''E'''('''x''', ''t'') and '''B'''('''x''', ''t''),  it holds that 
'''E'''(''λ'''''x''', ''λt'') and '''B'''(''λ'''''x''', ''λt'')  are also solutions.