Manifestly conformally covariant field theories

Abstract

In this thesis, a manifestly conformally covariant way of formulating free and interacting field theories is treated. The generators and the commutation relations of the conformal algebra are obtained and it is shown that the conformal group acts linearly in a six-dimensional space. This space has one extra time-like and one extra space-like dimension as compared to the ordinary four-dimensional space-time. This means that manifestly conformally covariant Lagrangians and field equations may be formulated. Projections from the six-dimensional conformal space to the four-dimensional Minkowski space are derived for both differential operators and fields. Manifestly covariant Lagrangians and field equations are given not only for free scalar, spinor and vector fields, but also for interacting field theories. The formalism is also applied to linearized gravitational fields in conformal gravity.