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Abstract

We investigate several quantum phenomena related to quadratic gravity after
rewriting the general fourth-order action in a more convenient form that is
second-order in derivatives and produces only first-class constraints in phase
space. We find that a Higgs mechanism may occur in the conformally invariant
subset of the general quadratic action if the theory is conformally coupled to
a scalar field that acquires a non-zero vacuum expectation value and
spontaneously breaks the conformal symmetry. Then, in the broken phase, the
originally massless spin-2 ghost may absorb both the scalar and vector fields
to become massive. We also perform a BRST quantization of second-order
quadratic gravity in the covariant operator formalism and discuss conditions
under which unitarity of the full interacting quantum theory may be
established.