The conformally invariant vector field on $R \times S^3$

In this diploma thesis vector field is constructed on $R \times S^3$. The free lagrangian on the curved space is invariant under conformal transformations of the dynamical field $A_m(x)$. The gauge fixing term is not conformally invariant, but it is invariant under Poincare transformations of the fields $A_m(x)$. Propagator quantisation is carried out. The energy spectrum of the physical subspace is analogous to the spectrum of flat quantum field theory.