In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the paper we discuss a limit process that allows to obtain also a Morse theory for li...

In this paper we present the full details of construction a Morse–Floer type homology related to superquadratic perturbation Dirac-geodesic model. This is computed explicitly using Leray–Serre spectral sequence and computation leads us several existence results Dirac-geodesics.