  When combining lumped mesoscopic electronic components to form a circuit,
quantum fluctuations of electrical quantities lead to a non-linear
electromagnetic interaction between the components that is not generally
understood. The Landauer-B\"uttiker formalism that is frequently used to
describe non-interacting coherent mesoscopic components is not directly suited
to describe such circuits since it assumes perfect voltage bias, i.e. the
absence of fluctuations. Here, we show that for short coherent conductors of
arbitrary transmission, the Landauer-B\"uttiker formalism can be extended to
take into account quantum voltage fluctuations similarly to what is done for
tunnel junctions. The electrodynamics of the whole circuit is then formally
worked out disregarding the non-Gaussianity of fluctuations. This reveals how
the aforementioned non-linear interaction operates in short coherent
conductors: voltage fluctuations induce a reduction of conductance through the
phenomenon of dynamical Coulomb blockade but they also modify their internal
density of states leading to an additional electrostatic modification of the
transmission. Using this approach we can account quantitatively for conductance
measurements performed on Quantum Point Contacts in series with impedances of
the order of $R_K = h / e^2$. Our work should enable a better engineering of
quantum circuits with targeted properties.
