  We consider a model of quantum-wire junctions where the latter are described
by conformal-invariant boundary conditions of the simplest type in the
multicomponent compactified massless scalar free field theory representing the
bosonized Luttinger liquids in the bulk of wires. The boundary conditions
result in the scattering of charges across the junction with nontrivial
reflection and transmission amplitudes. The equilibrium state of such a system,
corresponding to inverse temperature $\beta$ and electric potential $V$, is
explicitly constructed both for finite and for semi-infinite wires. In the
latter case, a stationary nonequilibrium state describing the wires kept at
different temperatures and potentials may be also constructed. The main result
of the present paper is the calculation of the full counting statistics (FCS)
of the charge and energy transfers through the junction in a nonequilibrium
situation. Explicit expressions are worked out for the generating function of
FCS and its large-deviations asymptotics. For the purely transmitting case they
coincide with those obtained in the litterature, but numerous cases of
junctions with transmission and reflection are also covered. The large
deviations rate function of FCS for charge and energy transfers is shown to
satisfy the fluctuation relations and the expressions for FCS obtained here are
compared with the Levitov-Lesovic formulae.
