Conformally Invariant Scalar-Tensor Field Theories in a Four-Dimensional Space

Understand

In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for a flat metric tensor and constant scalar field.

• It will be shown that all such field theories must be at most of fourth-order in the derivatives of the field variables.
• The Lagrangian of any such field theory can be chosen to be a linear combination of four conformally invariant scalar-tensor Lagrangians, with the coefficients being functions of the scalar field.
• Three of these "generating" Lagrangians are of second-order, while one of of third-order.