We analyze the implication of off-diagonal long-range order (ODLRO) for inhomogeneous periodic
field configurations and multi-component order parameters. For single component order parameters
we show that the only static, periodic field configuration consistent with ODLRO is a vortex lattice
with integer flux in units of the flux quantum in each unit cell. For a superconductor with g degenerate
components, fractional vortices are allowed. Depending on the precise order-parameter manifold,
they tend to occur in units of 1/g of the flux quantum. These results are well known to emerge from
the Ginzburg-Landau or BCS theories of superconductivity. Our results imply that they are valid even
if these theories no-longer apply. Integer and fractional vortex lattices are transparently seen to emerge
as a consequence of the macroscopic coherence and single valuedness of the condensat
