Tests of Lorentz Invariance Violation with Gamma Rays to probe Quantum Gravity

School of Physics & Center for Relativistic Astrophysics, Georgia Institute of Technology, 837 State Street, Atlanta GA 30332-0430 Department of Physics and Astronomy, Barnard College, Columbia University, NY 10027 Department of Physics and Astronomy, Van Allen Hall, University of Iowa, Iowa City, IA 52242 Physics Department, Washington University in St. Louis, 1 Brookings Dr., CB 1105, St. Louis, MO 63130 Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637 Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545 NASA Goddard Space Flight Center and University of California at Los Angeles Laboratoire Univers et Particules de Montpellier, Université Montpellier 2, CNRS/IN2P3, CC 72, Place Eugène Bataillon, F-34095 Montpellier Cedex 5, France Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439