Canonical transformation path to gauge theories of gravity II --- Spacetime coupling of spin-0 and spin-1 particle fields

Understand

The generic form of spacetime dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the Principle of General Relativity.

• It was thus shown that Einstein's General Relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the "free" (uncoupled) gravitational field, and (ii) the energy-momentum tensor is that of scalar fields representing real or complex structureless (spin-$0$) particles.
• It followed that all other source fields---such as vector fields representing massive and non-massive spin-$1$ particles---need careful scrutiny of the appropriate source tensor.
• This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field.