title: Quantum mechanics of 4-derivative theories.
abstract: A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
authors.affiliation: Departamento de Física Teórica, Universidad Autónoma de Madrid and Instituto de Física Teórica IFT-UAM/CSIC, Madrid, Spain.
authors.forename: Alberto
authors.initials: A
authors.lastname: Salvio
authors.affiliation: Dipartimento di Fisica dell'Università di Pisa and INFN, Pisa, Italy ; Theory Division, CERN, Geneva, Switzerland.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Strumia