  Scalar fields describe interesting phenomena such as Higgs bosons, dark
matter and dark energy, and are found to be quite common in physical theories.
These fields are susceptible to gravitational forces so that being massless is
not enough to remain conformal invariant. They should also be connected
directly to the scalar curvature. Because of this characteristics, we
investigated the structure and interactions of scalar fields under the
conformal transformations. We show how to reduce the quadratic quantum
contributions in the single scalar field theory. In the multi-scalar field
theories, we analyzed interactions in certain limits. We suggest a new method
for stabilizing Higgs bosons.
