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/root epsilon(0)mu(0) The other one, Z(0) = root mu(0)/epsilon(0) = 1/(c epsilon(0)) and its relation to the quantum vacuum, is discussed in this contribution. Deriving epsilon(0) from the properties of the quantum vacuum implies the derivation of the fine structure constant