Quantum field theory and classical optics: determining the fine   structure constant
  The properties of the vacuum are described by quantum physics including the response to external fields such as electromagnetic radiation. Of the two parameters that govern the details of the electromagnetic field dynamics in vacuum, one is fixed by the requirement of Lorentz invariance $c= 1/\sqrt{\varepsilon_{0} \mu_{0}}$. The other one, $Z_{0}= \sqrt{\mu_{0}/\varepsilon_{0}} = 1/(c\varepsilon_{0})$ and its relation to the quantum vacuum, is discussed in this contribution. Deriving $\varepsilon_{0}$ from the properties of the quantum vacuum implies the derivation of the fine structure constant. 
Gerd Leuchs, Margaret Hawton and Luis L. Sanchez-Soto
quant-ph