Schematic diagram
representing the base space M of
the vector bundle E,
a curve γ in M,
a pair of intersecting
coordinate patches O α and O ˜ α of M
that cover γ.
R is a point in O α ∩ O ˜ α .
The function π : E → M is
the bundle projection map that
maps the fiber V R
over R to R,
i.e., V R = π −1 ({R}).
H η and H are respectively
the typical fiber C N endowed with
the inner products η and
the Euclidean inner product .
The isomorphisms ϕ α,R : V R → H η and
ρ : H η → H
are unitary operators.