Higher time derivatives in effective equations of canonical quantum systems

TL;DR

This paper derives quantum-corrected equations of motion with higher time derivatives for canonically quantized systems, including anharmonic oscillators and implications for quantum gravity and cosmology.

Contribution

It provides a detailed derivation of higher time derivatives in effective equations for quantum systems, extending to systems relevant in gravity and cosmology.

Findings

Quantum corrections introduce higher time derivatives in equations of motion.

Derivations are exemplified with anharmonic oscillators.

Results have implications for quantum gravity and cosmological models.

Abstract

Quantum-corrected equations of motion generically contain higher time derivatives, computed here in the setting of canonically quantized systems. The main example in which detailed derivations are presented is a general anharmonic oscillator, but conclusions can be drawn also for systems in quantum gravity and cosmology.