  We formulate and apply a low-energy transport theory for hybrid quantum
devices containing junctions of topological superconductor (TS) wires and
conventional normal (N) or superconducting (S) leads. We model TS wires as
spinless $p$-wave superconductors and derive their boundary Keldysh Green's
function, capturing both the Majorana end state and continuum quasiparticle
excitations in a unified manner. We also specify this Green's function for a
finite-length TS wire. Junctions connecting different parts of the device are
described by the standard tunneling Hamiltonian. Using this Hamiltonian
approach, one also has the option to include many-body interactions in a
systematic manner. For N-TS junctions, we provide the current-voltage ($I$-$V$)
characteristics at arbitrary junction transparency and give exact results for
the shot noise power and the excess current. For TS-TS junctions, analytical
results for the thermal noise spectrum and for the $I$-$V$ curve in the
high-transparency low-bias regime are presented. For S-TS junctions, we compute
the entire $I$-$V$ curve and clarify the conditions for having a finite
Josephson current.
