https://doi.org/10.1140/epjc/s10052-016-4079-8
Regular Article - Theoretical Physics
Quantum mechanics of 4-derivative theories
1
Departamento de Física Teórica, Universidad Autónoma de Madrid and Instituto de Física Teórica IFT-UAM/CSIC, Madrid, Spain
2
Dipartimento di Fisica dell’Università di Pisa and INFN, Pisa, Italy
3
Theory Division, CERN, Geneva, Switzerland
* e-mail: alberto.salvio@cern.ch
Received:
1
March
2016
Accepted:
8
April
2016
Published online:
25
April
2016
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.
© The Author(s), 2016
