Limits on Lorentz and $CPT$ violation from double beta decay

Deviations from Lorentz and $CPT$ invariance in the neutrino sector and their observable effects in double beta decay are studied. For two-neutrino double beta decay, a spectral distortion and its properties are characterized for different isotopes. Majorana couplings for Lorentz violation are studied and shown to trigger neutrinoless double beta decay even for negligible Majorana mass. Existing data are used to obtain first limits of $5\times {10}^{-9}$ for 18 individual coefficients, and attainable sensitivities in current and future experiments are presented.