  It is shown that the elimination of the discrete transverse motion in a
waveguide of arbitrary shape may be described in terms of a non-abelian gauge
field for the longitudinal dynamics. This allows for an exact treatment of the
scattering between different modes by eliminating the gauge field at the
expense of a non-diagonal matrix of local subband energies. The method is
applied to calculate the local density of states (LDOS) in a quantum point
contact. Contrary to the total conductance which is well described by an
adiabatic approximation, mode mixing turns out to play a crucial role for local
properties like the LDOS.
