The Aharonov–Bohm effect can be understood from the fact that one can only measure absolute values of the wave function. While this allows for measurement of phase differences through quantum interference experiments, there is no way to specify a wavefunction with constant absolute phase. In the absence of an electromagnetic field one can come close by declaring the eigenfunction of the momentum operator with zero momentum to be the function "1" (ignoring normalization problems) and specifying wave functions relative to this eigenfunction "1". In this representation the i-momentum operator is (up to a factor ℏ ℏ / i ) the differential operator ∂ ∂ i = ∂ ∂ ∂ ∂ x i . However, by gauge invariance, it is equally valid to declare the zero momentum eigenfunction to be e − − i ϕ ϕ ( x ) at the cost of representing the i-momentum operator (up to a factor) as ∇ ∇ i = ∂ ∂ i + i ( ∂ ∂ i ϕ ϕ ) i.e. with a pure gauge vector potential A = d ϕ ϕ . There is no real asymmetry because representing the former in terms of the latter is just as messy as representing the latter in terms of the former. This means that it is physically more natural to describe wave "functions", in the language of differential geometry, as sections in a complex line bundle with a hermitian metric and a U(1)- connection ∇ ∇ . The curvature form of the connection, i F = ∇ ∇ ∧ ∧ ∇ ∇ , is, up to the factor i, the Faraday tensor of the electromagnetic field strength. The Aharonov–Bohm effect is then a manifestation of the fact that a connection with zero curvature (i.e. flat), need not be trivial since it can have monodromy along a topologically nontrivial path fully contained in the zero curvature (i.e. field-free) region. By definition this means that sections that are parallelly translated along a topologically non trivial path pick up a phase, so that covariant constant sections cannot be defined over the whole field-free region.