  The Faddeev-Popov gauge fixing in Yang-Mills theory is interpreted as
equivariant localization. It is shown that the Faddeev-Popov procedure amounts
to a construction of a symplectic manifold with a Hamiltonian group action. The
BRST cohomology is shown to be equivalent to the equivariant cohomology based
on this symplectic manifold with Hamiltonian group action. The ghost operator
is interpreted as a (pre)symplectic form and the gauge condition as the moment
map corresponding to the Hamiltonian group action. This results in the
identification of the gauge fixing action as a closed equivariant form, the sum
of an equivariant symplectic form and a certain closed equivariant 4-form which
ensures convergence. An almost complex structure compatible with the symplectic
form is constructed. The equivariant localization principle is used to localize
the path integrals onto the gauge slice. The Gribov problem is also discussed
in the context of equivariant localization principle. As a simple illustration
of the methods developed in the paper, the partition function of N=2
supersymmetric quantum mechanics is calculated by equivariant localization
