We present a method for constraining Lorentz violation in the electron
sector, based on observations of the photons emitted by high-energy
astrophysical sources. The most important Lorentz-violating operators at the
relevant energies are parameterized by a tensor c^{nu mu) with nine independent
components. If c is nonvanishing, then there may be either a maximum electron
velocity less than the speed of light or a maximum energy for subluminal
electrons; both these quantities will generally depend on the direction of an
electron's motion. From synchrotron radiation, we may infer a lower bound on
the maximum velocity, and from inverse Compton emission, a lower bound on the
maximum subluminal energy. With observational data for both these types of
emission from multiple celestial sources, we may then place bounds on all nine
of the coefficients that make up c. The most stringent bound, on a certain
combination of the coefficients, is at the 6 x 10^(-20) level, and bounds on
the coefficients individually range from the 7 x 10^(-15) level to the 2 x
10^(-17) level. For most of the coefficients, these are the most precise bounds
available, and with newly available data, we can already improve over previous
bounds obtained by the same methods.Comment: 28 page
