Quantum Inflation of Classical Shapes

TL;DR

This paper investigates how quantum shape dynamics can lead to a natural quantum inflation effect, causing early-time exponential divergence from classical evolution, with late-time behavior becoming increasingly classical.

Contribution

It demonstrates that quantum shape dynamics inherently produce quantum inflation, highlighting differences from traditional constrained Hamiltonian quantization approaches.

Findings

Wave-packets become more classical over time

Early-time semiclassical effects cause exponential scale mismatch

Quantum inflation occurs naturally in shape dynamics

Abstract

I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical system, occurs naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization.