Conformal invariance and the six-dimensional formalism

Conformal invariance is discussed assuming the equations are well defined in arbitrary coordinate systems. This assumption leads to some constraints on scale dimensions of terms, and constraints on the introduction of ‘conformally invariant massive equations’. The six-dimensional formalism is then discussed, and is generalized to project to all conformally flat spaces. Finally the imbedding of Minkowski space equations is studied.SO(4, 2) breaking is seen to enter due to the presence of a non-invariant scalar field, and a non-invariant vector field. The theorem relating invariance of the six-space equations underSO(4, 2) to the invariance of their corresponding four-space equations under the conformal group is carefully stated and proved.