Tests of Lorentz violation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>μ</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>e</mml:mi></mml:msub></mml:math>oscillations

A recently developed standard-model extension (SME) formalism for neutrino oscillations that includes Lorentz and $CPT$ violation is used to analyze the sidereal time variation of the neutrino event excess measured by the liquid scintillator neutrino detector (LSND) experiment. The LSND experiment, performed at Los Alamos National Laboratory, observed an excess, consistent with neutrino oscillations, of ${\overline{\ensuremath{\nu}}}_{e}$ in a beam of ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$. It is determined that the LSND oscillation signal is consistent with no sidereal variation. However, there are several combinations of SME coefficients that describe the LSND data; both with and without sidereal variations. The scale of Lorentz and $CPT$ violation extracted from the LSND data is of order ${10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{GeV}$ for the SME coefficients ${a}_{L}$ and $E\ifmmode\times\else\texttimes\fi{}{c}_{L}$. This solution for Lorentz and $CPT$ violating neutrino oscillations may be tested by other short baseline neutrino oscillation experiments, such as the MiniBooNE experiment.