Unitary Time Evolution and Vacuum for a Quantum Stable Ghost
Cédric Deffayet, Atabak Fathe Jalali, Aaron Held, Shinji Mukohyama, Alexander Vikman
TLDR
This paper quantizes a stable ghost system, demonstrating unitary time evolution and a well-defined vacuum through an integral of motion.
Key contributions
- Quantizes a classically stable system of a harmonic oscillator coupled to a ghost.
- Proves manifestly unitary time evolution and a well-defined quantum vacuum.
- Shows expectation values for squares of canonical variables are bounded.
- Confirms theoretical results with numerical solutions of the Schrödinger equation.
Why it matters
This work is crucial for understanding the quantization of systems involving "ghosts" or negative kinetic energy, which often lead to instabilities. By demonstrating unitary evolution and a stable vacuum, it offers a path towards consistent quantum theories for such systems.
Original Abstract
We quantize a classically stable system of a harmonic oscillator polynomially coupled to a ghost with negative kinetic energy. We prove that due to an integral of motion with a positive discrete spectrum: i) the Hamiltonian has a pure point spectrum unbounded in both directions, ii) the evolution is manifestly unitary, iii) the vacuum is well-defined, iv) expectation values for squares of canonical variables are bounded. Numerical solutions of the Schrödinger equation confirm these results. We argue that the discrete spectrum of the integral of motion enforces stability for extended interactions.
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