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Published March 15, 2009 | Published
Journal Article Open

Instabilities in the aether

Abstract

We investigate the stability of theories in which Lorentz invariance is spontaneously broken by fixed-norm vector "aether" fields. Models with generic kinetic terms are plagued either by ghosts or by tachyons, and are therefore physically unacceptable. There are precisely three kinetic terms that are not manifestly unstable: a sigma model (∂_µA_ν)^2, the Maxwell Lagrangian F_µνF^µν, and a scalar Lagrangian (∂_µA^µ)^2. The timelike sigma-model case is well defined and stable when the vector norm is fixed by a constraint; however, when it is determined by minimizing a potential there is necessarily a tachyonic ghost, and therefore an instability. In the Maxwell and scalar cases, the Hamiltonian is unbounded below, but at the level of perturbation theory there are fewer degrees of freedom and the models are stable. However, in these two theories there are obstacles to smooth evolution for certain choices of initial data.

Additional Information

© 2009 American Physical Society. Received 16 January 2009; published 13 March 2009. We are very grateful to Ted Jacobson, Alan Kostelecky, and Mark Wise for helpful comments. This research was supported in part by the U.S. Department of Energy and by the Gordon and Betty Moore Foundation.

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