Interactions of conformal and partially massless higher spin fields

This thesis investigates the interactions of partially massless (PM) fields in 4-dimensional (anti)de Sitter spaces, along with conformal higher spin fields and their coupling to matter in arbitrary dimensions. The first part of the thesis deals with PM fields and PM algebras. A reformulation of PM fields is proposed and studied using a novel chiral formulation, inspired by Penrose's twistor approach to massless fields in Minkowski space. This reformulation enables explicit construction of Yang-Mills-type interactions and current couplings. Next, an oscillator realisation for PM higher spin algebras is given in terms of bosonic and fermionic oscillators. The construction is based on the Weyl-Clifford algebra. The second part of the thesis derives the coupling between a massless scalar field and a background of higher spin fields within a manifestly covariant framework, employing Fedosov quantization techniques, called the "parent formulation". This formalism yields, in particular, an explicit covariant expression for the coupling between scalar fields and higher spin conformal gravity.