The Maslov correction in the semiclassical Feynman integral

The Maslov correction to the wave function is the jump of (-pi/2) in the phase when the system passes through a caustic. This can be explained by studying the second variation and the geometry of paths, as conveniently seen in Feynman's path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.