The paper by D. Colladay and V. Alan Kostelecký presents a Lorentz-violating extension of the minimal SU(3) × SU(2) × U(1) standard model, including both CPT-even and CPT-odd terms. This extension is motivated by the idea that the standard model may be the low-energy limit of a fundamental theory with Lorentz-covariant dynamics, where spontaneous Lorentz violation occurs. The extension maintains gauge invariance, energy-momentum conservation, and observer Lorentz covariance while breaking particle rotation and boost covariance. The quantized theory is hermitian and power-counting renormalizable, and it preserves desirable features such as microcausality, positivity of energy, and anomaly cancellation. The Higgs expectation value is shifted slightly, and the Z0 field acquires a small expectation. The authors derive a general Lorentz-breaking extension of quantum electrodynamics (QED) from this theory and consider experimental tests, particularly modifications to photon behavior, such as vacuum birefringence, which could be bounded from cosmological observations. Radiative corrections to the photon propagator are also examined, showing compatibility with spontaneous Lorentz and CPT violation at levels suggested by Planck-scale physics. The paper discusses the implications of these extensions for various experiments, including measurements of neutral-meson oscillations, tests of QED in Penning traps, and baryogenesis. It also addresses theoretical issues, such as the suppression of Lorentz violation at the electroweak scale and the role of spontaneous Lorentz violation in gravity at observable energies.The paper by D. Colladay and V. Alan Kostelecký presents a Lorentz-violating extension of the minimal SU(3) × SU(2) × U(1) standard model, including both CPT-even and CPT-odd terms. This extension is motivated by the idea that the standard model may be the low-energy limit of a fundamental theory with Lorentz-covariant dynamics, where spontaneous Lorentz violation occurs. The extension maintains gauge invariance, energy-momentum conservation, and observer Lorentz covariance while breaking particle rotation and boost covariance. The quantized theory is hermitian and power-counting renormalizable, and it preserves desirable features such as microcausality, positivity of energy, and anomaly cancellation. The Higgs expectation value is shifted slightly, and the Z0 field acquires a small expectation. The authors derive a general Lorentz-breaking extension of quantum electrodynamics (QED) from this theory and consider experimental tests, particularly modifications to photon behavior, such as vacuum birefringence, which could be bounded from cosmological observations. Radiative corrections to the photon propagator are also examined, showing compatibility with spontaneous Lorentz and CPT violation at levels suggested by Planck-scale physics. The paper discusses the implications of these extensions for various experiments, including measurements of neutral-meson oscillations, tests of QED in Penning traps, and baryogenesis. It also addresses theoretical issues, such as the suppression of Lorentz violation at the electroweak scale and the role of spontaneous Lorentz violation in gravity at observable energies.