"Lorentz invariance is one of the fundamental symmetries assumed by the Standard Model (SM) of particle physics. However, many extensions to the SM allow or predict Lorentz-invariance violation (LIV), in which this symmetry is either spontaneously broken or is only approximately valid at low energies. Under models in which LIV occurs in the photon sector, photon decay to electron/positron pair becomes allowed at sufficiently high energies. Astrophysical gamma (gamma) rays propagate over sufficient distances before reaching Earth that very nearly all of them should decay above the energy at which the decay becomes allowed. The detection of high-energy photons can therefore be used to constrain such models. The High-Altitude Water-Cherenkov (HAWC) observatory is a gamma-ray telescope located on the Sierra Negra volcano in the state of Puebla, Mexico. The detector consists of 300 water-filled tanks instrumented with four photomultiplier tubes each, which detect the Cherenkov light produced by charged particles in extensive air showers initiated by TeV cosmic gamma rays. This thesis presents an analysis of high-energy emission from several HAWC gamma-ray sources and sets new constraints on LIV-induced photon decay. This is done using a new algorithm for estimating the energies of gamma rays detected by HAWC, utilizing a neural network (NN) trained on Monte Carlo (MC) simulations of the detector. The NN uses a multilayer perceptron architecture and maps several geometric features of the air shower to an estimate of the primary photon's energy. HAWC's high-energy sensitivity combined with its improved energy resolution using the NN allows an LIV-induced cutoff in gamma-ray spectra below 209 TeV to be ruled out with 95% confidence. This corresponds to limits on the quantum-gravity energy scale of 8.74 x 1030 or 4.27 x 1022 eV for LIV perturbing the photon dispersion relation at first or second order respectively. These limits constitute a new best constraint on photon-sector LIV."--Pages ii-iii.
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