Gravitational contact interactions and the physical equivalence of Weyl transformations in effective field theory

Theories of scalars and gravity, with nonminimal interactions, ∼(M_P²+F (ϕ_i))R +L (ϕ_i), have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices, ∝q², that cancel the Feynman propagator denominator, 1 /q², and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as ∼F (ϕ_i)T_μ^μ(ϕ_i)/M_P² and F (ϕ_i)∂²F (ϕ_i)/M_P². The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the nonminimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such "hidden contact terms" one is compelled to go to the minimal Einstein-Hilbert representation.