Abstract
We investigate some quantum features of the bumblebee electrodynamics in
flat spacetimes. The bumblebee field is a vector field that leads to a
spontaneous Lorentz symmetry breaking. For a smooth quadratic potential,
the massless excitation (Nambu-Goldstone boson) can be identified as the
photon, transversal to the vacuum expectation value of the bumblebee
field. Besides, there is a massive excitation associated with the
longitudinal mode and whose presence leads to instability in the
spectrum of the theory. By using the principal-value prescription, we
show that no one-loop radiative corrections to the mass term is
generated. Moreover, the bumblebee self-energy is not transverse,
showing that the propagation of the longitudinal mode cannotbe excluded
from the effective theory. (C) 2015 The Authors. Published by Elsevier
B.V.
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