  We give a functional analytical proof of the equality between the Maslov
index of a semi-Riemannian geodesic and the spectral flow of the path of
self-adjoint Fredholm operators obtained from the index form. This fact,
together with recent results on the bifurcation for critical points of strongly
indefinite functionals (see P. M. Fitzpatrick, J. Pejsachowicz, L. Recht,
Spectral Flow and Bifurcation of Strongly Indefinite Functionals Part I.
General Theory, J. Funct. Anal. 162 (1) (1999), 52-95.) imply that each non
degenerate and non null conjugate (or $P$-focal) point along a semi-Riemannian
geodesic is a bifurcation point.
