Classical and quantum ghosts
Abstract
The aim of these notes is to provide a selfcontained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated with a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we do not consider very ad hoc choices, compatibility with observational constraints implies that low energy effective ghosts can exist only at the price of giving up Lorentz invariance or locality above the cutoff, in which case the cutoff has to be much lower that the energy scales we currently probe in particle colliders. We also comment on the possible role of extra degrees of freedom which break Lorentz invariance spontaneously.
 Publication:

European Journal of Physics
 Pub Date:
 January 2015
 DOI:
 10.1088/01430807/36/1/015009
 arXiv:
 arXiv:1406.4550
 Bibcode:
 2015EJPh...36a5009S
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 14 pages, PDFLateX, version accepted for publication in the European Journal of Physics