  In the context of conventional quantum field theory, we present a general
Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model
including CPT-even and CPT-odd terms. It can be viewed as the low-energy limit
of a physically relevant fundamental theory with Lorentz-covariant dynamics in
which spontaneous Lorentz violation occurs. The extension has gauge invariance,
energy-momentum conservation, and covariance under observer rotations and
boosts, while covariance under particle rotations and boosts is broken. The
quantized theory is hermitian and power-counting renormalizable, and other
desirable features such as microcausality, positivity of the energy, and the
usual anomaly cancellation are expected. Spontaneous symmetry breaking to the
electromagnetic U(1) is maintained, although the Higgs expectation is shifted
by a small amount relative to its usual value and the $Z^0$ field acquires a
small expectation. A general Lorentz-breaking extension of quantum
electrodynamics is extracted from the theory, and some experimental tests are
considered. In particular, we study modifications to photon behavior. One
possible effect is vacuum birefringence, which could be bounded from
cosmological observations by experiments using existing techniques. Radiative
corrections to the photon propagator are examined. They are compatible with
spontaneous Lorentz and CPT violation in the fermion sector at levels suggested
by Planck-scale physics and accessible to other terrestrial laboratory
experiments.
