Spontaneous Lorentz violation requires determining the vacuum from the Hamiltonian density rather than the Lagrangian potential minimum, ruling out quadratic potentials and allowing only stable timelike or lightlike VEVs for smooth potentials.
The simplest realization of such a potential is the cubic formV(X) = λ 3 X 3 withλ >0
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Hamiltonian Constraints on Spontaneous Lorentz Symmetry Breaking in the Bumblebee Model
Spontaneous Lorentz violation requires determining the vacuum from the Hamiltonian density rather than the Lagrangian potential minimum, ruling out quadratic potentials and allowing only stable timelike or lightlike VEVs for smooth potentials.