2015/12/31 by Alberto Salvio, Alessandro Strumia, Алессандро Струмиа · 93 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Classical mechanics #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Gravitation #Graviton #Kinetic term #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Theoretical physics #Unitary state #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1140/epjc/s10052-016-4079-8
published in The European Physical Journal C 76(4), 227 (Springer Science+Business Media) · 25 pages. v2: clarifications added, final published version
openalex publication_date 2016/04/01 · arxiv created 2016/04/19 · arxiv updated 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.