  We introduce a `proper time' formalism to study the instability of the vacuum
in a uniform external electric field due to particle production. This formalism
allows us to reduce a quantum field theoretical problem to a quantum-mechanical
one in a higher dimension. The instability results from the inverted oscillator
structure which appears in the Hamiltonian. We show that the `proper time'
unitary evolution splits into two semigroups. The semigroup associated with
decaying Gamov vectors is related to the Feynman boundary conditions for the
Green functions and the semigroup associated with growing Gamov vectors is
related to the Dyson boundary conditions.
