Quantum mechanics of 4-derivative theories

Understand

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 quantisation.

• 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, normalisable wave functions, unitary evolution in a negative-norm configuration space.
• We present a formalism for quantum mechanics with a generic norm.