  A microscopic analysis of the superconducting quantum critical point realized
via a pair-breaking quantum phase transition is presented. Finite temperature
crossovers are derived for the electrical conductivity, which is a key probe of
superconducting fluctuations. By using the diagrammatic formalism for
disordered systems, we are able to incorporate the interplay between
fluctuating Cooper pairs and electrons, that is outside the scope of a
time-dependent Ginzburg Landau or effective bosonic action formalism. It is
essential to go beyond the standard approximation in order to capture the zero
temperature correction which results purely from the (dynamic) quantum
fluctuations and dictates the behavior of the conductivity in an entire low
temperature quantum regime. All dynamic contributions are of the same order and
conspire to add up to a negative total, thereby inhibiting the conductivity as
a result of superconducting fluctuations. On the contrary, the classical and
the intermediate regimes are dominated by the positive bosonic channel. Our
theory is applicable in one, two and three dimensions and is relevant for
experiments on superconducting nanowires, doubly-connected cylinders, thin
films and bulk in the presence of magnetic impurities, magnetic field or other
pair-breakers. A window of non-monotonic behavior is predicted to exist as
either the temperature or the pair-breaking parameter is swept.
