This thesis contains two parts. The first part deals with
pion-nucleon/meson-baryon scattering in the Kadyshevsky formalism. This
formalism is introduced and discussed. Problems may arise when derivative
couplings and/or higher spin fields are used, especially when compared to the
results in the Feynman formalism: unwanted contact terms pop-up. These terms
are cancelled using the Gross and Jackiw or Takahashi and Umezawa method. The
final results in both formalisms are therefore equal, causal and covariant.
Formal incorporation of pair suppression in the baryon exchange sector is
achieved using a method based on the Takahashi and Umezawa method. For the
resulting tree level amplitudes, we have shown, to our knowledge for the first
time, that they are causal, covariant and n-independent. Moreover, the
amplitudes are just a factor 1/2 of the usual Feynman expressions. The
amplitudes contain only posititve energy initial and final states, although it
should be mentioned that negative energy is present inside an amplitude via the
Delta propagator. The second part of this thesis deals with higher spin field
quantization in the framework of Dirac's Constraint analysis. A full constraint
analysis and quantization procedure is presented for the free spin 1,3/2 and 2
case and for the situation where these fields are coupled to auxiliary fields.
The constructed propagators in the former case are shown to be non-covariant,
as is well-known. Therefore, auxiliary fields coupled to gauge conditions of
the free case are introduced in the Lagrangian. Now, the resulting propagators
are covariant.Comment: 189 page