Classical and Quantum Dynamics of Higher-Derivative Systems

TL;DR

This paper reviews higher-derivative systems in physics, discusses the problematic ghosts they involve, and speculates that our universe might be a classical solution within a benign higher-derivative theory in higher dimensions.

Contribution

It provides a review of higher-derivative systems, analyzes conditions for benign ghosts, and proposes a speculative higher-dimensional framework for the universe.

Findings

Higher-derivative systems involve ghosts with unbounded Hamiltonians.

Certain special cases feature benign ghosts that do not cause collapse.

The universe may be a classical solution in a higher-derivative bulk theory.

Abstract

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however: ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe represents then a classical solution in this theory, having the form of a 3-brane embedded in the bulk.