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 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.

25 pages. v2: clarifications added, final published version

References in corpus (14)

• Making Sense of Non-Hermitian Hamiltonians
• Avoiding Dark Energy with 1/R Modifications of Gravity
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Einstein Gravity from Conformal Gravity
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model
• Solution to the ghost problem in fourth order derivative theories
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity
• Unitarity in the Brout-Englert-Higgs Mechanism for Gravity
• Classically Scale Invariant Inflation, Supermassive WIMPs, and Adimensional Gravity
• Giving up the ghost
• The Transactional Interpretation of Quantum Mechanics and Quantum Nonlocality
• Advancing the case for $PT$ Symmetry -- the Hamiltonian is always $PT$ Symmetric

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