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arXiv · 1512.01237

Quantum mechanics of 4-derivative theories

Alberto Salvio·Alessandro Strumia
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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.

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Alberto Salvio, Alessandro Strumia. 2016-04-19. Quantum mechanics of 4-derivative theories. https://doi.org/10.1140/epjc%2Fs10052-016-4079-8

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