Description
I will discuss stable systems with ghosts and how they can even become more stable upon quantization. This stability is due to the existence of a positive definite integral of motion. I will show how to canonically quantize a classically stable system of a harmonic oscillator polynomially coupled to a ghost with an unbounded-below kinetic energy. I will prove that i) the integral of motion has a positive discrete spectrum, ii) the Hamiltonian has a point spectrum unbounded in both directions, iii) the evolution is manifestly unitary, iv) the vacuum is well-defined, and v) the squared canonical variable expectation values remain bounded. Numerical solutions of the Schrödinger equation confirm these results. I will argue that the discrete spectrum of the integral of motion enforces stability for extended interactions.