prediction of the decay times exceeds the scope of this article. A discussion of this topic can be found in ref. [@Lasenby:2002mc]. The topic of the summer project as presented here is based on refs. [@Lasenby:2002mc; @Soffel:1977wn; @Soffel:1982pm] and therefore owes many ideas to these papers where the present problems have been treated for the first time. A similar situation concerning the Klein-Gordon equation has been considered in ref. [@Deruelle:1974zy].

Implementation of general relativity into the Dirac equation
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Since we are going to study a fermion in a gravitational field we have to consider the coupling of the Dirac equation to gravity. According to the other fundamental interactions occurring in nature gravity can also be formulated as a gauge theory. (For an introduction to the idea of gauge theories in general we suggest ref. [@[book6]](Chapter 15).) The difference is that not local invariance under internal symmetric transformations is demanded but local invariance under Lorentz transformations is considered.

Notation
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The following symbols will be used:

-   $\psi$ $\hat =$ Dirac Spinor (in coordinate representation).

-   $|\Psi\rangle$ $\hat =$ vector in Hilbert space describing an arbitrary quantum state and $\langle\Psi |$ $\hat =$ the corresponding dual vector (refraining from any 